Cole rewrote a quadratic function in vertex form. h(x)=x^2 -6x+7
Cole said that the vertex is (3, 2). Is Cole correct? If not, identify the step in which Cole made the mistake and correct his work.
Cole is incorrect. The vertex form of a quadratic function is given by h(x) = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola.
To rewrite the given quadratic function in vertex form, we need to complete the square. Here is the correct step-by-step process:
h(x) = x^2 -6x + 7
h(x) = (x^2 - 6x + 9) - 9 + 7
h(x) = (x-3)^2 - 2
Therefore, the correct vertex form of the quadratic function is h(x) = (x-3)^2 - 2. This means the correct vertex is (3, -2), not (3, 2) as Cole stated.