Algebra two question

Question

Inez throws a ball upward from her apartment balcony and the ball falls to the ground below. The height of the ball above the ground in feet is modeled by the quadratic , where t is the time in seconds that the ball is in the air. Find the vertex, the y-intercept, and the zeros. Explain what each means in terms of the problem. Are both zeros appropriate? Why or why not?

Answer 1

Since the equation is given to you in Standard Format, it would be easiest just to find the X vertex first (then plug that value into the equation and solve for Y to find the coordinate of the vertex).

1. X = -b/2a; -32/(2)(-162); X = -32/-324; X = .099 plug this into find y vertex
2. Y = -162(.099)² +32(.099) +48
3. Y = 49.58 feet
4. Vertex is: (.099, 49.58) the maximum height of the ball (49.58') happens .099 seconds after the throw
5. Y intercept is when X=0, so Y intercept=48, it's starting position (he was a very bad thrower, only picked up a foot and a 1/2!)
6. To find the zeros, factor or use quadratic equation and you will find X ≅ -.45, X ≅ .65
7. However both zeros are not appropriate as there will not be negative "time" so at .65 seconds the ball will hit the ground