Cole is incorrect. The mistake is in Step 2 where Cole added 7 and then subtracted 9 without factoring out the 9 first.
The correct steps are:
Step 1: h(x) = x^2 − 6x + 7
Step 2: h(x) = (x^2 − 6x + 9) + 7 - 9
h(x) = (x - 3)^2 - 2
So, the correct vertex is (3, -2), not (3, 2).
Cole rewrote a quadratic function in vertex form.
h(x)= x2−6x+7
Step 1: h(x)= (x2−6x+ 9 )+7
Step 2: h(x)=(x2−6x+ 9 )+7 −9
Step 3: h(x)=(x−3 )2+2
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.
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