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.
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).