Question

For the function f(x) = -16/2025 x^2 + 9/5 x + 2.5, what is the vertex form of the equation?

A) f(x) = -16/2025 (x - h)^2 + k, where (h, k) is the vertex.
B) f(x) = -16/2025 (x + h)^2 + k, where (h, k) is the vertex.
C) f(x) = -16/2025 (x - h)^2 - k, where (h, k) is the vertex.
D) f(x) = -16/2025 (x + h)^2 - k, where (h, k) is the vertex.

Answer 1

The vertex form of the given quadratic equation is f(x) = -16/2025 (x - h)^2 + k.

Step-by-step explanation:

The vertex form of a quadratic equation is given by the formula f(x) = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex. In the given equation, f(x) = -16/2025 x^2 + 9/5 x + 2.5, the coefficient of x^2 is a = -16/2025. To find the vertex form, we need to complete the square.

Step 1: Divide the coefficient of x by 2 and square it to determine the value of h.

Step 2: Add and subtract h from the equation.

Step 3: Factor the quadratic expression and simplify.

Based on these steps, the correct vertex form of the equation is option A) f(x) = -16/2025 (x - h)^2 + k, where (h, k) represents the vertex.