Question

A graph of a quadratic function has its vertex at the point (-8,6). The graph of the function passes through the point (7,9). When written in vertex form, the function has the form f(x)=a(x−h) 2 +k. Determine the following values and enter the value of a as a fraction. a= h= k=

Answer 1

To determine the values of a, h, and k in the equation f(x) = a(x - h)^2 + k, we can use the information given about the vertex and a point on the graph. Given that the vertex is (-8,6), we can determine that h = -8 and k = 6. The quadratic function passes through the point (7,9), which allows us to find the value of a.

Step-by-step explanation:

To determine the values of a, h, and k in the equation f(x) = a(x - h)² + k, we can use the information given about the vertex and a point on the graph.

Given that the vertex is (-8,6), we can determine that h = -8 and k = 6.

The quadratic function passes through the point (7,9), which allows us to find the value of a. By substituting the values of x and f(x) into the equation, we get 9 = a(7 - (-8))² + 6. Solving for a, we get a = 3/225.