Question

1)

A car magazine wants to determine the maximum rpm of a car. The following graph shows the equation y=−2x2+8x
. The equation represents the function for the rpm of the car in thousands, where the rpm is y
and the number of seconds is x
.





The maximum rpm for the car is

(1 point)
Responses

6,000 rpm
6,000 rpm

8,000 rpm
8,000 rpm

10,000 rpm

Answer 1

The maximum rpm for the car can be determined by finding the vertex of the parabola represented by the equation y = -2x^2 + 8x. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -2 and b = 8. Plugging in the values, we get x = -8 / (2*-2) = 2.

Substitute x = 2 back into the equation to find the maximum rpm: y = -2*(2)^2 + 8*2 = -2(4) + 16 = -8 + 16 = 8,000 rpm.

So, the correct answer is 8,000 rpm.

Answer 2

The engine returns to idle and the rpm becomes 0 at(1 point)
Responses

2 seconds
2 seconds

3 seconds
3 seconds

4 seconds

Answer 3

The engine returns to idle and the rpm becomes 0 when y = 0.

0 = -2x^2 + 8x

0 = -2x(x - 4)

This equation will be true when either x = 0 or x = 4.

So, the engine returns to idle at 4 seconds.

Therefore, the correct answer is:

4 seconds

Answer 4

The rpm of the car increases for the first(1 point)
Responses

2 seconds
2 seconds

3 seconds
3 seconds

4 seconds

Answer 5

The rpm of the car increases when the value of y is positive. Therefore, we need to find when y (the rpm) is greater than 0. Going back to the equation -2x^2 + 8x:

-2x^2 + 8x > 0

Solving this inequality gives us x > 0 or x < 4. The rpm is increasing in the interval from 0 to 4 seconds.

Therefore, the rpm of the car increases for the first 4 seconds.

So, the correct answer is:

4 seconds