Question

Calculate the vertex of h(t) = - 16t^2 + 24t + 300

Answer 1

Answer: (-0.75, 309)

Explanation:

To find the vertex, first we will complete the square.

Given:

h(t) = - 16t² + 24t + 300

Factor out -16:

h(t) = -16(t² - 1.5t) + 300

Add and subtract
`(b)/(2) ^2`:

h(t) = -16(t² - 1.5t + 0.5625 - 0.5625) + 300

Regroup:

-16 * -0.5625 = 9; 9 + 300 = 309

h(t) = -16(t² - 1.5t + 0.5625) + 309

Factor:

h(t) = -16(t² - 1.5t + 0.5625) + 309

h(t) = -16(t - 0.75)² + 309

Now, this equation is in vertex form. The vertex is (h, k) in the form y = a(x - h)² + k, meaning that our vertex is;

(-0.75, 309)

I have also graphed this, see attached.