Question

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

Answer 1

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

Answer 2

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

Answer 3

so plug in the numbers

Answer 4

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

Answer 5

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

Answer 6

not sure what did you do?

Answer 7

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

Answer 8

The answer is 18.1 :}