Question

The function h(x) = -16x² + 48x + 1 represents the height, in feet, of a toy rocket x seconds

after being launched. Which statement is true?
A The rocket attains its highest elevation after 37 seconds.
B The rocket hits the ground after approximately 3 seconds.
C The rocket is launched from an initial height of 16 feet.
D The rocket's highest elevation is approximately 1.5 feet.

Answer 1

The rocket attains its highest elevation after 1.5 seconds.

Step-by-step explanation:

The function h(x) = -16x² + 48x + 1 represents the height, in feet, of a toy rocket x seconds after being launched. To determine which statement is true, we need to analyze the function.

To find the highest elevation of the rocket, we need to find the vertex of the quadratic function. The x-coordinate of the vertex is given by the formula x = -b/(2a), where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c.

For the function h(x) = -16x² + 48x + 1, the vertex is (1.5, h(1.5)). Therefore, the rocket attains its highest elevation after 1.5 seconds.