Which is the graph of f(x)=(x-1)(x+4)
Answers
The quadratic function is described by the standard equation [tex]\boxed{ \ f(x) = ax^2 + bx + c \ }.[/tex]
We have the quadratic function [tex]\boxed{ \ f(x) = (x - 1)(x + 4) \ }.[/tex]
Let us configure it to obtain a standard equation.
[tex]\boxed{f(x) = (x - 1)(x + 4)}[/tex]
[tex]\boxed{f(x) = x^2 + 4x - x - 4}[/tex]
Hence, we get [tex]\boxed{\boxed{ \ f(x) = x^2 + 3x - 4 \ }}.[/tex]
We identify the coefficients a, b, and c. For this equation, [tex]\boxed{ \ a = 1, b = 3, and \ c = -4 \ }[/tex]The parabola opens upward because a > 0, resulting in a vertex that is a minimum.The y-intercept of the quadratic function f(x) = x² + 3x - 4 is (0, c), i.e., the point [tex]\boxed{ \ (0, -4) \ }.[/tex]From [tex]\boxed{ \ f (x) = (x - 1)(x + 4) \ }[/tex] we get the x-intercepts at [tex]\boxed{ \ (-4, 0) \ and \ (1, 0) \ }[/tex]The axis of symmetry is [tex]\boxed{ \ x = h = -\frac{b}{2a} \ }[/tex], i.e., [tex]\boxed{ \ x = h = -\frac{3}{2(1)} \rightarrow h = -\frac{3}{2} \ }[/tex]The minimum value is [tex]\boxed{ \ k = -\frac{25}{4} = -6\frac{1}{4} \ }[/tex]The vertex is [tex]\boxed{ \ (h, k) \ },[/tex] where [tex]\boxed{ \ k = f(h) \ }[/tex] or [tex]\boxed{ \ k = \frac{b^2 - 4ac}{-4a} \ }[/tex]Finding the minimum value is as follows:
[tex]\boxed{ \ k = f (- \frac{3}{2}) = (- \frac{3}{2})^2 + 3(- \frac{3}{2}) - 4 = -\frac{25}{4} = -6\frac{1}{4} \ }, or[/tex][tex]\boxed{ \ k = \frac{3^2 - 4(1)(-4)}{-4(1)} = -\frac{25}{4} = -6\frac{1}{4} \ }[/tex]Notes:
The graph of a quadratic function is called a parabola.When a > 0, the parabola opens upward, resulting in a vertex that is a minimum.When a < 0, the parabola opens downward, resulting in a vertex that is a maximum.The value c is the y-intercept of the graph, because a y-intercept is a point on the graph where x is zero. In other words, the graph passes through the point [tex]\boxed{ \ (0, c) \ }.[/tex]From [tex]\boxed{ \ f (x) = (x - x_1)(x - x_2) \ }[/tex] we get x-intercepts at [tex]\boxed{ \ (x_1, 0) \ and \ (x_2, 0) \ }.[/tex] An x-intercept represents a point on the graph where y is zero.The axis of symmetry represent the line that passes through the vertex of parabola with equation [tex]\boxed{ \ x = h = -\frac{b}{2a} \ }[/tex]The vertex is [tex]\boxed{ \ (h, k) \ },[/tex] where [tex]\boxed{ \ k = f(h) \ }[/tex] or [tex]\boxed{ \ k = \frac{b^2 - 4ac}{-4a} \ }[/tex]Learn moreA line that is not parallel to either the x-axis or the y-axis https://brainly.com/question/4691222 Finding the y-intercept of the quadratic function f(x) = (x – 6)(x – 2) https://brainly.com/question/1332667The midpoint https://brainly.com/question/3269852Keywords: which is the graph of f(x) = (x - 1)(x + 4), the x-intercept, quadratic function, a standard equation, the y-intercept, the axis of symmetry, the vertex, parabola, upward, downward
The graph of f(x) = (x-1)(x+4) is an upward-opening parabola with roots at x = 1 and x = -4. It should be plotted carefully, labeling and scaling the axes to show maximum and minimum values, and ensuring it passes through the roots with the proper shape.
Explanation:The graph of the function f(x) = (x-1)(x+4) can be determined by finding the roots and the shape of the curve. The roots of the function can be found when f(x) = 0, which occurs at x = 1 and x = -4. Therefore, these are the points at which the graph will intersect the x-axis. Since it's a quadratic function, its graph will be a parabola.
Additionally, because the coefficient of x² is positive, the parabola opens upwards. To graph this function accurately, one needs to plot the roots and then sketch the parabola, ensuring that it intersects these points and opens upwards. The vertex of the parabola can also be found by averaging the roots, which gives us the x-value of the vertex as (-4 + 1)/2 = -1.5, with the corresponding y-value obtained by evaluating f(x) at x = -1.5.
The resulting graph would start above the x-axis for x < -4, pass through the x-axis at x = -4, reach a vertex at x = -1.5, pass through the x-axis again at x = 1, and continue upwards for x > 1.
The graph should be accurately scaled and labeled with the function f(x) and the variable x, and include the maximum and minimum values on the axes based on the calculated points and the behavior of the quadratic function.
Related Questions
Steven earns money babysitting. He charges 31.25 for 5 hours and 50 for 8 hours explain what the constant rate of change means I this coming tent
Answers
What is Szymborska's overall opinion of humanity in "A Contribution to Statistics?" Support your response with at least two details or quotes from the poem.
Answers
Answer:
Szymborska's overall opinion of humanity in "A Contribution to Statistics" is overall positive
Step-by-step explanation:
Szymborska is a poet who likes to comment on society with irony and sarcasm.One example of this is when she splits people into categories in her poem “A Contribution to Statistics”. Here Szymborska’s overall opinion of humanity may seem negative due to her bluntness and dry humor. For example, she says in the tenth stanza, “cruel when forced by circumstances -better not to know even ballpark figures.” It’s implied in this line that most people (maybe even all)are cruel or can be. She also says, “taking only things from life -thirty”which comments how lots of people are selfish. However, this seemingly cynical poem takes a sweeter turn near the end with statistics like, “worthy of compassion - ninety-nine” and “mortal- a hundred out of a hundred.” These lines reveal that even though Szymborska believes that humanity is extremely flawed the mass majority of us deserve and are worthy of love. Plus the fact that we’re all mortal may seem dark but the fact remains that both the righteous and the sinners will all end up in the same place. The fact that no one can escape
death gives humans equality in a way. Szymborska’s overall opinion of humanity turned out to be more optimistic after all.
Nick has 3.90 in quarters and dimes total number of coins is 27how many quarters and dimes
Answers
Answer:
8 quarters; 19 dimes trust me i checked
Step-by-step explanation:
A man notices that a tank is half full. After emptying 600 litres from the tank, that it is now one-third full. How much does the tank hold when it is full?
Answers
One third is equal to 2/6.
After removing 600 litres from the tank, there is a decrease from 3/6 to 2/6
3/6-2/6=1/6
600 litres is 1/6 of the tank. Multiply by 6 to get the capacity of a full tank.
600*6=3600
The tank can hold 3600 litres.
After removing 600 litres from a tank that was half full, it became one-third full. By setting up an equation, we determine that every 600 litres represents one-sixth of the tank's full capacity. Multiplying 600 litres by 6, we find the tank's full capacity is 3600 litres.
The question involves determining the total capacity of a tank based on information given about volume reductions and proportions of fullness. Initially, the tank is half full, but after removing 600 litres, it becomes one-third full. We can set up an equation to find out the total capacity of the tank (T).
Since removing 600 litres takes the tank from being half full to one-third full, that means 600 litres correspond to one-sixth of the tank's capacity because one half minus one-third equals one-sixth.
Now we set up our equation: 600 litres = T/6. To solve for T, we multiply both sides of the equation by 6:
(600 litres)* 6 = T3600 litres = T
Therefore, the full capacity of the tank is 3600 litres.
What is 39 percent of 120?
Answers
In the figure, which of the following edges is skew to edge AD?
edge BC
edge HD
edge GC
edge EH
...?
Answers
The edge that is skew to edge AD is edge GC
What are skew edges?In geometry, skew edges refer to edges that are not in the same plane and do not intersect. They belong to non-coplanar lines or segments, implying that they extend in different directions. Skew lines, and consequently their edges, never meet and remain at a constant distance from each other.
From the figure
line AD and GC are Skew since they can never meet yet they are not parallel to each other.
Skew lines are non-intersecting, non-coplanar lines in three-dimensional space. They neither share common points nor lie in the same plane, demonstrating their distinct orientation and lack of intersection in a three-dimensional geometric context.
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Parallelograms can be used to prove statements about triangles.
True False
Answers
Answer:
it's true
Step-by-step explanation:
The triangles made by diagonal parallelograms will be congruent so we can prove statements so will be True.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
As per the parallelogram drawn.
ΔABC ≅ ΔADC (By SAS postulute of congruency)
So we can make the statement that the two triangles made by the diagonal of a parallelogram will be congruent.
Hence "The triangles made by diagonal parallelograms will be congruent so we can prove statements so will be True".
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Help needed :/
(1/2^-2) + 1/2
A. 2
B. 2 1/2
C. 4
D. 4 1/2
Answers
C. 4 (not to be confused with the explosive... :P)
Firewood is often sold by the cord a cord is wood is abby doe measuring 4 feet by 4 feet by 8 feet what's the volume of a cord of wood in cubic feet?
Answers
An airplane takes off with a full tank of 40,000 gallons of fuel and flies at an average speed of 550 miles per hour. After 8 hours in flight, there are 14,000 gallons of fuel left. It will take another 3.5 hours for the plane to reach its destination. How much fuel will be left in the tank when the plane lands? What is the total distance of the flight?
Answers
1. The quantity of fuel left in the tank when the plane lands will be 3,375 gallons.
2. The total distance of the flight is 6,325 miles.
How are the quantities determined?The quantities are computed using basic mathematical operations, including subtraction, division, addition, and multiplication.
Full tank of the airplane = 40,000 gallons
Average speed = 550 miles per hour
Number of hours on first flight = 8 hours
The quantity of fuel left = 14,000
The quantity of fuel consumed in 8 hours = 26,000 (40,000 - 14,000)
The quantity of fuel consumed per hour or per 550 miles = 3,250 miles (26,000 ÷ 8)
Additional hours on the final flight = 3.5 hours
The quantity of fuel consumed during the final flight = 11,375 gallons (3.5 x 3,250)
The total quantity of fuel consumed for the flight = 37,375 gallons (26,000 + 11,375)
The quantity of fuel left after the flight = 2,625 gallons (40,000 - 37,375)
The total hours for the flight = 11.5 hours (8 + 3.5)
The total distance of the flight = 6,325 miles (550 x 11.5)
Mathematically, after flying 11.5 hours or 6,325 miles, the airplane consumed 37,375 gallons of fuel, leaving only 2,625 gallons in its tank.
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calculate the mean 12,2,8,6,57
Answers
85/5= 17
mean=17
(12+2+8+6+57)/5=85/5=17
the mean is 17
The function p(t) represents the value of a new car t years after it was manufactured.
p(t)=24,525(0.94)^t
What does the value 0.94 represent in this situation?
The value of the car increases by 94% each year.
The initial value of the car is 0.94.
The value of the car is 0.94 times the value of the car the previous year.
The value of the car decreases by 94% each year.
I think its D
Answers
Answer:
The value of the car is 0.94 times the value of the car the previous year.
Answer:
Option C is correct
The value of the car is 0.94 times the value of the car the previous year.
Step-by-step explanation:
Given the function:
[tex]p(t) = 24,525(0.94)^t[/tex]
where,
p(t) represents the value of a new car
t is the number of years.
We have to find the value 0.94 represent in this situation.
For t =0 years.
Initial value of car p(0) is 24,525
For t = 1 years
[tex]p(1) =24,525 \cdot 0.94[/tex]
For t = 2 years
[tex]p(2) =24,525 \cdot (0.94)^2[/tex] and so on...
Since;
[tex]\frac{p(2)}{p(1)} = 0.94[/tex]
⇒[tex]p(2) = 0.94 \cdot p(1)[/tex]
In general:
[tex]p(t) = 0.94 \cdot p(t-1)[/tex] where, t is the number of years.
⇒the value of the car is 0.94 times the value of the car the previous year.
If trapezoid JKLM is translated according to the rule (x, y) → (x + 2, y − 6), what are the coordinates of point L'?
(1, −4)
(−4, −1)
(−7, 4)
(0, 7)
Answers
(1,-4)
Answer:
A. (1,-4)
Step-by-step explanation:
L= (-1, 2)
(x,y)>(x+2, y-6)
(x,y)>(-1+2, 2-6)
(x,y)>(1, -4)
Name the property of real numbers illustrated by the equation.
[tex] \pi +10 = 10 + \pi [/tex]
Answers
It doesn't matter which order the numbers are added in, the same result will be achieved.
1+2 = 2+1
2*4 = 4*2
Answer:
commutative property
Step-by-step explanation:
Given equation: [tex]\pi+10=10+\pi[/tex]
The property of real number used in this equation is Commutative property
Commutative property : A binary operation [tex]{\displaystyle *}[/tex] on a set is commutative if [tex]a {\displaystyle *}b= b{\displaystyle *}a[/tex]
Following this property [tex]\pi+10=10+\pi[/tex]
If
f (n)(0) = (n + 1)!
for
n = 0, 1, 2, ,
find the Maclaurin series for f.
Answers
The Maclaurin series for f(n) is 1.
Explanation:The Maclaurin series for a function can be found using the formula: f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...
In this case, f(0) = (0+1)! = 1, f'(0) = d/dx((0+1)!) = d/dx(1) = 0, f''(0) = d^2/dx^2((0+1)!) = d^2/dx^2(1) = 0, and so on.
Using these values, the Maclaurin series for f(n) is: f(n)(x) = 1 + 0x + 0x^2/2! + 0x^3/3! + ... = 1.
How do the CHNOPS elements create macromolecules?
plzzzz helppppp
Answers
Here, they obtain it through various means... like carbon & oxygen from atmosphere, hydrogen from water, nitrogen & phosphorus from soil & sometimes by eating insects (Venus Fly trap).
So, in short, your answer is by complex process of photosynthesis.
Hope this helps!
mark estimates that the distance from his house to to his school is 15.5 mi the actual distance is 14.5 mi to the nearest tenth of a percent what is the percent error in Mark's estimate?
ANWSER ONLY IF U KNOW THE ANWSER GOT IT!!!!! please help
Answers
The percent error in Mark's estimate to the nearest tenth of a percent is 6.9%.
What is Percentage?Percentage is the ratio such that it can be expressed as a fraction of 100. Percentage is calculated by dividing the number with the whole and then multiplying by 100.
The symbol used to denote percentage is '%'.
Percent error is the absolute value calculated by finding the difference of the estimated value and the actual value and then dividing by the actual value followed by multiplication with 100.
Percent Error = [(Estimated value - Actual value) / Actual value] × 100
= [(15.5 - 14.5) / 14.5] × 100
= (1 / 14.5) × 100
= 6.897%
≈ 6.9%
Hence, there is a 6.9% percent error in Mark's estimate if his estimated distance from his house to the school is 15.5 m and the actual distance is 14.5 m.
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The percent error in Mark's estimate is 6.9%.
To calculate the percent error, we use the formula:
[tex]\[ \text{Percent Error} = \left( \frac{\text{Estimated Value} - \text{Actual Value}}{\text{Actual Value}} \right) \times 100\% \][/tex]
Given the estimated distance is 15.5 mi and the actual distance is 14.5 mi, we can plug these values into the formula:
[tex]\[ \text{Percent Error} = \left( \frac{15.5 \text{ mi} - 14.5 \text{ mi}}{14.5 \text{ mi}} \right) \times 100\% \][/tex]
[tex]\[ \text{Percent Error} = \left( \frac{1 \text{ mi}}{14.5 \text{ mi}} \right) \times 100\% \][/tex]
[tex]\[ \text{Percent Error} \approx \left( \frac{1}{14.5} \right) \times 100\% \][/tex]
[tex]\[ \text{Percent Error} \approx 0.069 \times 100\% \][/tex]
[tex]\[ \text{Percent Error} \approx 6.9\% \][/tex]
Therefore, the percent error in Mark's estimate is approximately 6.9%.
93 /100 converted to percent equals? ...?
Answers
Solve for x: 3x + 4 = 5(x − 8)
Answers
3x + 4 = 5x - 40
- 3x
4 = 2x - 40
+ 40
44 = 2x
÷ 2
22 = x
Hope this helps!
distribute the 5 to x and -8 and you'd get
3x + 4 = 5x-40 then subtract 4 from both sides getting
3x = 5x-44 then subtract 5x from both sides getting
8x = -44 then divide both sides by 8 getting
x = -5.5
nonzero abscissa, negative ordinate
a.Quadrant II or Quadrant IV
b.Quadrant I or Quadrant II
c.Quadrant I or Quadrant IV
d.Quadrant III or Quadrant IV ...?
Answers
Nonzero abscissa, negative ordinate is located in Quadrant III or Quadrant IV.
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D.) Quadrant lll or Quadrant IV
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is this correct ?
....
Answers
_________________
Answer choice: [C]: "The patient has the flu."
______________________
is INCORRECT."
_______________________
The answer is that: "No conclusions can be found." ; or
____________________________
"Not possible."
_____________________________
Your answer is incorrect because we cannot conclude from the statements given that the "patient has the flu".
_____________________________
We are given the following statements:
_______________________________
1) The doctor recommends rest if the patient has the flu.
2) The doctor recommends rest.
_______________________________
We know that: "The doctor recommends rest"; however, the doctor could be "recommending rest" for numerous other reasons; even if the patient does not have the flu.
______________
Likewise, Answer choice: [B]: "If the doctor recommends rest, the patient has the flu."
__________________
is incorrect for essentially the same reason that "Answer choice: [C]" is incorrect.
__________________
Consider answer choice: [D]: The patient does not have the flu.
______________________
This answer choice is incorrect. We cannot conclude that the patient does not have the flu. We cannot determine, from the statements provided, whether the patient does or does not have the flu.
__________________________________________
So this leaves us with: Answer choice: [A]: not possible (to reach a conclusion).
____________________________________________
hope this helps you
Forty-four percent of the members of the Science Club wear blue shirts. Which of the following is a binomial experiment? A.Selecting eight members randomly and recording whether each member is wearing a blue shirt
B.Selecting eight members randomly and recording the number in the group wearing a blue shirt
C.Selecting members randomly until one without a blue shirt is chosen
D. Selecting members randomly until one with a blue shirt is chosen
Answers
Answer:
Option A is correct.
Step-by-step explanation:
Selecting eight members randomly and recording whether each member is wearing a blue shirt.
A binomial experiment is defined as a statistical experiment which consists of n repeated trials. Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.
Here, in 8 members the person wearing blue will be a success others will be a failure outcome.
What can each term of the equation be multiplied by to eliminate the fractions before solving? x – 2x = x 2 6 10 12
Answers
Answer:
12
Step-by-step explanation:
I did the test
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply.
y = –x + 1
3x − 4y = −4
4x − 3y = −3
y – 2 = –(x – 4)
y + 2 = (x + 4)
Answers
To find a line parallel to a given line and passing through a certain point, determine the slope of the given line, rearrange it to slope-intercept form, then substitute the point's coordinates to find the y-intercept of the parallel line.
To find a line parallel to the given line, we need the same slope of 3. Start by rearranging the given equation 3x - 4y = 7 to slope-intercept form: y = (3/4)x - 7/4. Since the parallel line passes through (-4,-2), substitute these values into the slope-intercept form to find the y-intercept. The equation of the line parallel to 3x - 4y = 7 that passes through (-4,-2) is y = (3/4)x + 2.
solve for X. 4 = log2x
Answers
The value of x to solve the given equation is 16.
The given equation is:
[tex]log_2x=4[/tex]
What is a logarithm function?A logarithm function is a special style to write an exponential function.
For example, If [tex]a^x=b[/tex] then we write it as [tex]log_ab=x[/tex].
So, [tex]log_2x=4[/tex] can be written as:
[tex]2^4=x[/tex]
Or, [tex]x=2^4[/tex]
[tex]x=16[/tex]
So, the value of x =16.
Hence, the value of x to solve the given equation is 16.
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Name the property of equality that justifies: (I have to put question into an equation below because I can't get it in this question without it being confusing)
A. Addition Property of Equality
B. Subtraction Property of Equality
C. Multiplication Property of Equality
D. Division Property of Equality
If:
m
then
5×m
Answers
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Trip walks a total of 12 miles to and from school each week. Lindsey rides her bike a total of 56 miles to and from school each week.
Use the greatest common factor and the distributive property to complete the equation, and find the total number of miles Trip and Lindsey travel to and from school each week.
(3 + ) =
Answers
the total number of miles is
12 miles + 56 miles
so 12 + 56 = 3x4 +14x4= 4x(3+14)
the anser is 4x(3+14) = 68
Final answer:
The total number of miles Trip and Lindsey travel to and from school each week is 68 miles, determined by using the greatest common factor of 12 and 56, which is 4, and the distributive property to group and multiply the sum of the unit contributions by 4.
Explanation:
To find the total number of miles Trip and Lindsey travel to and from school each week using the greatest common factor (GCF) and the distributive property, we first identify the GCF of the two numbers. The GCF of 12 and 56 is 4. We can then apply the distributive property to factor out the GCF and write the equation as follows:
(3 + 14) × 4 = total number of miles traveled to and from school each week.
Trip contributes '3' units of the GCF and Lindsey contributes '14' units of the GCF. To find the total, we add 3 and 14 to get 17, and then multiply by the GCF:
17 × 4 = 68
Therefore, Trip and Lindsey travel a total of 68 miles to and from school each week.
Slingerland borrowed $8,000 on july 20, at 11% interest. if the loan was due on october 17, what was the amount of interest on the loan using the exact interest method?
Answers
I think the answer is $216.99 ?
Answer:
The amount of interest on the loan was of $214.57.
Step-by-step explanation:
Slingerland borrowed $8,000 at an 11% interest rate, thus having to pay $880 after a year.
As the loan was due on October 17, and the difference between July 20 and October 17 is of 89 days, using the exact interest method we can affirm that:
880 / 365 x 89 = X
2.41 x 89 = X
$214.57 = X
The amount of interest on the loan was of $214.57.
Jason has already read 27 pages of a book. He plans to read 3 pages of the book every day. If f(n) represents the total number of pages that Jason will complete reading in n days, which of the following functions represents the relationship between f(n) and n?
f(n) = 27n − 3
f(n) = 3n − 27
f(n) = 27n + 3
f(n) = 3n + 27
Answers
27 would be the Y intercept, and 3n would be the slope.
f(n) = 3n + 27
Answer:
D.[tex]f(n)=3n+27[/tex]
Step-by-step explanation:
Total number of pages in a book=f(n)
Jason has already read pages=27
He plans to read pages of the book everyday=3
He takes times to complete reading the book=n days
He read pages in n days=3n
We have to find the function which represents the relationship between f(n) and n.
According to question information
[tex]f(n)=3n+27[/tex]
This is required relation between f(n) and n.
Answer:D.[tex]f(n)=3n+27[/tex]
which two numbers multiply to get 140 and add to get 39
Answers
35 + 4= 39