Question

if a quadratic equation models the path of a basketball shot and the equation is $y = -5x^2 + 25x + 2$, at what point does the basketball reach its maximum height?
a. $x = 2$
b. $x = 3$
c. $x = 5$
d. $x = 2.5$

Explanation:

Step1: Identify quadratic coefficients

For $y = ax^2 + bx + c$, here $a=-5$, $b=25$.

Step2: Calculate vertex x-coordinate

Use vertex formula $x = -\frac{b}{2a}$
$x = -\frac{25}{2\times(-5)} = \frac{25}{10} = 2.5$

Answer:

d. $x = 2.5$