Question

The path of a football kicked by a field goal kicker can be modeled by the equation y = –0. 03x2 1. 53x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the football’s maximum height? Round to the nearest tenth. Yds. How far is the football kicked? yds.

Answer 1

The ball travels 51 yards in total.

What is a parabola?

The path of a projectile under the influence of gravity follows a curve of this shape.

This is the equation of an upside-down parabola, so the maximum height will be at the vertex.

To find the vertex, we'll use the formula for the x-coordinate and then solve for the y-coordinate.

$\rm x=\dfrac{-1.53}{2-0.3}\\\\x=25.5$

Plugging this into the given formula:

$\rm y = -0.03x^2 + 1.53x\\\\y = -0.03(25.5)^2+1.53(25.5)\\\\y=19.50$

The maximum height would be 20 yards.

To find how far the football travels in total, we need to set the equation equal to 0 and find the roots:

$\rm 0=-0.03x^2+1.53x\\\\x(-0.03x+1.53)=0\\\\ x= 0\\\\-0.03x=-1.53\\\\x= \dfrac{-1.53}{-0.03}\\\\x=51$

Hence, the ball travels 51 yards in total.

To know more about Parabola click the link given below.

https://brainly.com/question/8495268