Question

F(t)= (t-5)² - 9 what are the zeros of the function?

Smaller T:
Larger t:
What is the vertex of the parabola?: (__,__)

Answer 1

The zeros of the function f(t) = (t-5)² - 9 are t = 2 and t = 8, with the smaller t being 2 and the larger t being 8. The vertex of the parabola is at the point (5, -9).

Step-by-step explanation:

The question asks us to find the zeros of the function f(t) = (t-5)² - 9 and the vertex of the parabola represented by this function. To find the zeros, we need to solve the equation (t-5)² - 9 = 0. This can be done by setting the quadratic equal to zero and factoring, or using the quadratic formula.

Setting the inside of the parentheses equal to the square root of 9, we get two equations: t - 5 = 3 and t - 5 = -3. Solving for t in each equation gives us the zeros: t = 8 and t = 2. Therefore, the smaller t is 2, and the larger t is 8.

The vertex of a parabola in the form f(t) = a(t-h)² + k is at the point (h, k). For the function f(t), the vertex is thus at (5, -9).