Cole rewrote the quadratic function h(x) = x^2 - 6x +7 into vertex form, Cole said the vertex is (3.2) is he correct? Show your work
First, let's rewrite the quadratic function h(x) = x^2 - 6x + 7 in vertex form:
h(x) = (x - 3)^2 - 9 + 7
h(x) = (x - 3)^2 - 2
So, the vertex is at (3, -2), not (3,2). Cole is incorrect.
You forgot to identify the which STEP in which Cole made a mistake and correct his work.
Apologies for the oversight. Let's correct and identify the error in Cole's work:
Given quadratic function: h(x) = x^2 - 6x + 7
To rewrite the function in vertex form, we complete the square:
h(x) = (x^2 - 6x + 9) + 7 - 9
h(x) = (x - 3)^2 - 2
Now, comparing this form with the vertex form:
h(x) = a(x - h)^2 + k
We see that Cole made a mistake in identifying the correct vertex. The correct vertex is at (3, -2), not (3,2). Cole's answer was incorrect.
Therefore, the corrected statement is: Cole's mistake occurred in identifying the correct vertex. The correct vertex for the function h(x) = x^2 - 6x + 7 is (3, -2).