## anonymous one year ago Darlene kicks a soccer ball off the ground and in the air, with an initial velocity of 34 feet per second. Using the formula H(t) = −16t2 + vt + s, what is the maximum height the soccer ball reaches? 17.7 feet 18.1 feet 19.3 feet 20.2 feet

1. freckles

If you find the vertex of the parabola you can find the max height.

2. freckles

$H(t)=-16t^2+v_0t+h_0 \\ \text{ where } v_0 \text{ is initial velocity } \\ \text{ and } h_0 \text{ is the initial height } \\ \text{ you are given } v_0=34 \frac{\text{ ft}}{\text{ sec}} \\ \text{ and the inital height was given as zero since that is where the ball started at } \\ \text{ you know on the ground }$

3. freckles

so plug in the numbers

4. freckles

and then write into the vertex form let me know if you need any help

5. anonymous

So the answer is C correct or did i do the math wrong.

6. freckles

not sure what did you do?

7. freckles

$ax^2+bx+c \\ a(x^2+\frac{b}{a}x)+c \\ a(x^2+\frac{b}{a}x+(\frac{b}{2a})^2)+c-a(\frac{b}{2a})^2 \\ a(x+\frac{b}{2a})^2+c-a(\frac{b}{2a})^2 \\ \text{ vertex of } ax^2+bx+c \text{ is } (-\frac{b}{2a},c-a (\frac{b}{2a})^2) \\ \text{ the \max is given by the y-coordinate }$

8. anonymous