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25.10.2020

Which statements are true about the parabola represented by the equatlon y = 3x 2 -15x+30

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24.06.2023, solved by verified expert

Ranjana Bhatt

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Y = 3x² - 15x + 30
y = 3(x² - 5x) + 30
y = 3(x² - 5x + (5/2)²) + 30
y = 3(x - 5/2)² + 30
The parabola opens upwards. Vertex at (5/2, 30)

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Mathematics

Which statements are true about the parabola represented by the equation y=−3x^2+18x+23 Select all that apply. 1. The leading coefficient is positive, so the parabola opens up. 2. The leading coefficient is negative, so the parabola opens down. 3. The parabola has a maximum. 4. The parabola has a minimum.

Step-by-step answer

P Answered by Specialist

2, 3

Step-by-step explanation:

2. The leading coefficient is -3. When the leading coefficient is negative, the parabola opens down.

3. When the parabola opens down, it has a maximum point, but no minimum point. (when the parabola opens up, it has a minimum, but no maximum)

I hope this helps :)

Mathematics

Step-by-step answer

P Answered by Master

2, 3

Step-by-step explanation:

2. The leading coefficient is -3. When the leading coefficient is negative, the parabola opens down.

3. When the parabola opens down, it has a maximum point, but no minimum point. (when the parabola opens up, it has a minimum, but no maximum)

I hope this helps :)

Mathematics

Which statements are true about the parabola represented by the equatlon y = 3x 2 -15x+30

Step-by-step answer

P Answered by PhD

Y = 3x² - 15x + 30
y = 3(x² - 5x) + 30
y = 3(x² - 5x + (5/2)²) + 30
y = 3(x - 5/2)² + 30
The parabola opens upwards. Vertex at (5/2, 30)

StudenGPT

Select the correct answer. Marcel is performing the first test on his company s new electric car. During the test, the electric car reaches a maximum speed of 81 mph. The performance test results of the electric car can be modeled by the following graph, where x represents time, in seconds at the start of the test, and y represents the speed, in miles per hour. The graph shows a downward parabola vertex at (6, 80). The parabola starts from the origin, passes through (3, 60), (9, 60), and ends at (12, 0) Which of the following statements is true

Step-by-step answer

P Answered by Studen AI

To determine the correct answer, let's analyze the given information about the graph of the electric car's speed during the test:

1. The graph is a downward parabola, which means it opens downwards like a U-shape.
2. The vertex of the parabola is at (6, 80), which means at 6 seconds the car is traveling at 80 mph. This is the maximum speed achieved by the car during the test.
3. The parabola starts from the origin, meaning at the beginning of the test (0 seconds), the car has a speed greater than 0 mph.
4. The parabola passes through the points (3, 60) and (9, 60), which means the car's speed at 3 seconds and 9 seconds is 60 mph.
5. The parabola ends at (12, 0), which means at 12 seconds, the car comes to a stop and its speed is 0 mph.

Based on this information, we can determine the correct answer by reasoning through the options:

A. The electric car is not moving at 4 seconds and 8 seconds.
- This statement is not correct because there is no specific information provided for the car's speed at 4 seconds and 8 seconds.

B. The electric car is not moving at 6 seconds and 12 seconds.
- This statement is not correct because the car is not stationary (speed = 0 mph) at 12 seconds. The car comes to a stop at 12 seconds but was moving prior to that.

C. The electric car is not moving at 0 seconds and 12 seconds.
- This statement is not correct because the car starts from the origin (0 seconds) with a speed greater than 0 mph. Additionally, as mentioned before, the car is not stationary (speed = 0 mph) at 12 seconds.

D. The electric car is not moving at 0 seconds and 6 seconds.
- This statement is correct based on the information provided. The car starts from the origin (0 seconds) and reaches its highest speed at 6 seconds (80 mph), indicating that it was in motion from the start. It is reasonable to conclude that the car was not stationary (speed = 0 mph) at 0 seconds and 6 seconds.

Therefore, the correct answer is D. The electric car is not moving at 0 seconds and 6 seconds.

Mathematics

PLS ANSWER CORRECTLY The function f(x) = –3x2 + 36x – 119 written in vertex form is f(x) = –3(x – 6)2 – 11. Which statements are true about the graph of f(x)? Select three options. A. The axis of symmetry is the line x = 6. B. The vertex of the graph is at (–6, –11). C. The parabola has a minimum. D. The parabola opens down. E. The value of h, when the equation is written in vertex form, is positive.

Step-by-step answer

P Answered by PhD

A. The axis of symmetry is the line x = 6.

D. The parabola opens down.

E. The value of h, when the equation is written in vertex form, is positive.

Step-by-step explanation:

f(x) = –3(x – 6)^2 – 11.

This is in vertex form

y = a( x-h)^2 +k

where ( h,k) is the vertex

(6,-11) is the vertex, so line line of symmetry is x=6

a =-3 so the parabola opens down and it has a maximum

The value of h is 6, which is the x coordinate of the vertex

Mathematics

The function p(x) = 6x2 + 48x written in vertex form is p(x) = 6(x + 4)2 – 96. which statements are true about the graph of p? check all that apply. a) the axis of symmetry is the line x = –4. b) the graph is narrower than the graph of f(x) = x2. c) the parabola has a maximum. d) the parabola opens down. e) the value of k is –96, so there is a vertical shift down 96 units.

Step-by-step answer

P Answered by Master

The correct options are A, B and E.

Step-by-step explanation:

The given function is

p(x)=6x^2+48x

Vertex form of the function is

p(x)=6(x+4)^2-96 ..... (1)

The vertex form of a parabola is

f(x)=a(x-h)^2+k ..... (2)

where, (h,k) is vertex and x=h is the axis of symmetry.

If a>0, then parabola opens up and if a<0, then parabola opens down.

If |a|>1, then graph is narrower than the graph of f(x)=x^2 and if |a|<1, then graph is wider than the graph .

From (1) and (2), it is clear that

a=6, h=-4, k=-96

So we conclude that

1. The axis of symmetry is the line x = –4.

2. The graph is narrower than the graph of f(x)=x^2 .

3. The parabola has a minimum.

4. The parabola opens up.

5. The value of k is –96, so there is a vertical shift down 96 units.

Therefore options A, B and E are correct.

Mathematics

The function g(x) = 10x2 – 100x + 213 written in vertex form is g(x) = 10(x – 5)2 – 37. which statements are true about g(x)? check all that apply. 1-the axis of symmetry is the line x = –5. 2-the vertex of the graph is (5, –37). 3-the parabola has a minimum. 4-the parabola opens up. 5-the value of a, when the equation is written in vertex form, is negative.

Step-by-step answer

P Answered by Specialist

The correct options are

(2) The vertex of the graph is (5, –37).

(3) The parabola has a minimum.

(4) The parabola opens up.

Step-by-step explanation: Given that the function g(x)=10x^2-100x+213 is written as follows in the vertex form :

g(x)=10(x-5)^2-37~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We are to select all the correct options.

We know that

for the STANDARD equation of a parabola, i.e., $f(x)=a(x-h)^2+k,[\tex]</p<p<strongthe axis of symmetry is</strong [tex]x-h=0,$

the vertex of the parabola is (h, k),

the parabola has a minimum and opens up if a is positive, the parabola has a maximum and opens down if a is negative.

Comparing the equation (i) with the standard vertex form, we get

the axis of symmetry is given by

$x-5=0\\\\\Rightarrow x=5.$

The vertex of the parabola will be

(h, k) = (5, -37).

Since the value of a is 10, positive, so the parabola has a minimum and opens up.

Thus, the correct options are

(2) The vertex of the graph is (5, –37).

(3) The parabola has a minimum.

(4) The parabola opens up.

Mathematics

Step-by-step answer

P Answered by Specialist

The axis of symmetry is the line x = 6.

The parabola opens down.

The value of h, when the equation is written in vertex form, is positive.

Step-by-step explanation:

Because it is... :)

Mathematics

The function f(x) = –3x2 + 36x – 119 written in vertex form is f(x) = –3(x – 6)2 – 11. which statements are true about the graph of f(x)? check all that apply. the axis of symmetry is the line x = 6. the vertex of the graph is at (–6, –11). the parabola has a minimum. the parabola opens down. the value of h, when the equation is written in vertex form, is positive.

Step-by-step answer

P Answered by PhD

Analysis:

f(x) = –3(x – 6)^2 – 11

means vertex is at x = 6 and y = - 11

The negative sign in front of x^2 means the parabola opens downward.

The, the vertex is a maximum point, which is below the x-axis (because it is negative). Therefore the parabola do not cross the x-axis, meaning that all the y-values are negative (≤ -11).

Options:

The axis of symmetry is the line x = 6.---> true, the symetry line is vertical and passes through the vertex

The vertex of the graph is at (–6, –11).---> false, it is (6, -11)

The parabola has a minimum.---> false, y values have not a lower bound.

The parabola opens down.---> true, because the negative sign in front ox x^2

The value of h, when the equation is written in vertex form, is positive. ---> false, the value of h is positive. It is 6. Although h is preceeded by a negative sign in the equation, h itself is positive.

Mathematics

Step-by-step answer

P Answered by Master

The correct options are

(2) The vertex of the graph is (5, –37).

(3) The parabola has a minimum.

(4) The parabola opens up.

Step-by-step explanation: Given that the function g(x)=10x^2-100x+213 is written as follows in the vertex form :

g(x)=10(x-5)^2-37~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We are to select all the correct options.

We know that

for the STANDARD equation of a parabola, i.e., $f(x)=a(x-h)^2+k,[\tex]</p<p<strongthe axis of symmetry is</strong [tex]x-h=0,$