Question

The vertex of a quadratic function is (6, 2), and the y-intercept of the function is (0,

-70). The equation of the function in vertex form, fx)=a(x-h' +k, is shown
What is the value of a?

Answer 1

To find the value of 'a' in the vertex form of a quadratic function with the vertex (6, 2) and the y-intercept (0, -70), substitute the y-intercept into the equation and solve for 'a'. The result is a = -2.

Step-by-step explanation:

The question at hand is to determine the value of a in the vertex form of a quadratic function, f(x) = a(x - h)^2 + k, given the vertex (6, 2) and the y-intercept (0, -70). We know that in the vertex form, h and k correspond to the coordinates of the vertex, thus indicating that in this function, (h, k) is (6, 2).

To find the value of a, we can use the y-intercept. We substitute the y-intercept's x-value, which is 0, and its y-value, which is -70, into the vertex form equation. We then solve for a.

The steps are:

Substitute the y-intercept into the vertex form: -70 = a(0 - 6)^2 + 2.

Solve for a: -70 = a(36) + 2 → -72 = 36a → a = -2.