Question

A construction worker tosses a brick with a height function h(t)=−5t2−20t+105. Rewrite the function in a different form and find the height of the brick at its highest point.

a. Vertex form; 80 meters
b. Factored form; 105 meters
c. Standard form; -20 meters
d. None of the above

Answer 1

The height function of the brick can be rewritten as h(t) = -5(t^2 + 4t) + 105. The height of the brick at its highest point is 80 meters.

Step-by-step explanation:

The height function of the brick is given by h(t) = -5t^2 - 20t + 105. To rewrite it in vertex form, we complete the square by grouping the quadratic terms: h(t) = -5(t^2 + 4t) + 105. To find the maximum height, we need to find the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/2a. In this case, a = -5 and b = -20:
t = -(-20)/(2(-5)) = 2. Substitute t = 2 back into the height function: h(2) = -5(2^2) - 20(2) + 105 = 80.