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.

1 answer

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).