Question

Maggie is throwing a ball into the air and catching it. The height of Maggie’s ball is modeled by the function h(t) = –16t2 + 48t + 15.

Part 1. Which ball goes higher in the air, the ball that is hit or the ball that is thrown? Use complete sentences and show all work to explain how you determined the height that each ball reaches.

Answer 1

I really need help in math could some one please explain to me how to solve this.

Answer 2

It seems like part of the question is missing but I'll try to answer. The function you've presented can show you the height of the ball at any given time t. If you solve for h(t) = 0 using the quadratic formula, then you will get two values (positive and negative). The positive value will be your time (t), when the ball is at it's highest point based on the initial velocity of the ball at time zero. You just need to plug that value into the equation to get your max height. The initial velocity is fixed by the equation, so if this equation represents a thrown ball, then one that is hit will have a faster or slower velocity based on how hard it is hit (the initial velocity). Hopefully this helps you some.

Quadratic formula:
\[x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]
where the initial equation take the form:
\[ax^2+bx+c\] which yours does. Your x's are just t's. You can memorize the quadratic equation by singing it to the tune 'pop goes the weasel' ( http://www.youtube.com/watch?v=2lbABbfU6Zc).