Question

REINFORCE A Roman candle firework is launched from a platform 5 feet above the

ground. The firework has an initial velocity of 150 feet per second. A function that
models the firework's vertical distance with respect to time, t, is h(t) = -16t2 + 150t + 5.
. What is the vertex form of this quadratic function? Round to the hundredths place.

Answer 1

The vertex form of the quadratic function h(t) = -16t^2 + 150t + 5 is -16(t - 2.34)^2 + 238.59, found by completing the square and rounding to hundredths.

Step-by-step explanation:

The given quadratic function that models the firework's vertical distance is h(t) = -16t2 + 150t + 5. To convert this to vertex form, we complete the square:

1. Factor out the coefficient of the t2 term from the first two terms:
2. -16(t2 - (150/16)t) + 5
3. Add and subtract the square of half the coefficient of t inside the parentheses:
4. -16(t2 - (150/16)t + (150/32)2 - (150/32)2) + 5
5. Simplify inside the parentheses to get the perfect square trinomial and adjust the constant term:
6. -16((t - 75/32)2 - (75/32)2) + 5
7. Continue simplifying:
8. -16(t - 75/32)2 + 16(75/32)2 + 5
9. Do the arithmetic:
10. h(t) = -16(t - 2.34375)2 + 233.59375 + 5
11. h(t) = -16(t - 2.34)2 + 238.59 (rounded to hundredths)

Thus, the vertex form of the function h(t) is -16(t - 2.34)2 + 238.59.