Question

41. Henry stands on a platform and shoots a rocket in his 10th
grade science class. He found that the motion of the rocket can be
described by the equation y = 60 + 28x – x2, where y is the
vertical distance and x is the horizontal distance traveled. If this
trajectory equation were to be graphed, find the x-intercepts of the
equation. (Fun fact: The positive x-intercept is how far away from
the platform the rocket hits the ground!)

Answer 1

The x-intercepts of the quadratic equation are given by x = -2 and x = 30.

What are the x-intercepts of a quadratic equation?

A quadratic equation is modeled by:

y = ax² + bx + c.

The x-intercepts are the values of x when y = 0, given by:

$x_1 = \frac{-b + \sqrt{\Delta}}{2a}$

$x_2 = \frac{-b - \sqrt{\Delta}}{2a}$

In which:

$\Delta = b^2 - 4ac$

In this problem, the equation is:

y = 60 + 28x - x².

Hence the coefficients are a = -1, b = 28, c = 60.

Then:

$\Delta = 28^2 - 4(-1)(60) = 1024$

$x_1 = \frac{-28 + \sqrt{1028}}{-2} = -2$

$x_2 = \frac{-28 - \sqrt{1028}}{-2} = 30$

The x-intercepts of the quadratic equation are given by x = -2 and x = 30.

More can be learned about quadratic equations at https://brainly.com/question/24737967