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.
graph (0,0) (1,6)(2,8)(3,6)(4,0)
The maximum rpm for the car is
A. 6,000 rpm
B. 8,000 rpm
C. 10,000 rpm
B. 8,000 rpm
The maximum rpm of the car occurs at the vertex of the parabolic graph. In this case, the vertex is at x=2, which corresponds to 8,000 rpm (y=8).
The engine returns to idle and the rpm becomes 0 at
A. 2 seconds
B. 3 seconds
C. 4 seconds
C. 4 seconds
The rpm of 0 occurs when y=0. From the graph, we can see that the rpm becomes 0 at x=4 seconds.
The rpm of the car increases for the first
A. 2 seconds
B. 3 seconds
C. 4 seconds
B. 3 seconds
From the graph, we can see that the rpm of the car starts increasing from 0 rpm at x=0 (start point) and reaches its maximum at x=2 (vertex). So, the rpm of the car increases for the first 3 seconds until it reaches the maximum rpm at x=2.
its 2 seconds
I apologize for the error in my previous response. Let's reevaluate the situation.
Given the equation y = -2x^2 + 8x represents the rpm of the car, the rpm starts increasing from 0 rpm at x = 0 (start point) and reaches its maximum at the vertex.
To find out when the rpm starts increasing, we need to look at when the derivative of the function is positive. The derivative of the function y with respect to x is dy/dx = -4x + 8.
Setting dy/dx > 0 will show when the rpm starts increasing:
-4x + 8 > 0
4x < 8
x < 2
This means that the rpm starts increasing in the first 2 seconds, and not 3 seconds as previously mentioned.
Therefore, the correct answer is:
A. 2 seconds
seconds, then it decreases for the next blank seconds
2 seconds
3 seconds
4 seconds
seconds, then it decreases for the next 2 seconds
Given the equation y = -2x^2 + 8x represents the rpm of the car, the rpm starts increasing from 0 rpm at x = 0 (start point) and reaches its maximum at the vertex at x=2. The rpm then decreases after the vertex.
To find out when the rpm starts decreasing, we need to look at when the derivative of the function changes sign. The derivative of the function y with respect to x is dy/dx = -4x + 8.
Setting dy/dx < 0 will show when the rpm starts decreasing:
-4x + 8 < 0
4x > 8
x > 2
This means that the rpm starts decreasing after 2 seconds.
Therefore, the rpm increases for the first 2 seconds, then it decreases for the next 2 seconds.
he axis of symmetry is
A. 2 seconds
B. 3 seconds
C. 4 seconds