Felicia rewrote a quadratic function in vertex form.

Question

h(x)= x^2−6x+7

Step 1: h(x)= (x^2−6x+ 9 )+7

Step 2: h(x)=(x^2−6x+ 9 )+7 −9

Step 3: h(x)=(x−3 )^2+2
Felicia said that the vertex is (3, 2). Is Felicia correct? If not, identify the step in which Felicia made the mistake and correct her work.

Answer 1

Felicia is incorrect. The mistake is in Step 2 where she added 7 and then subtracted 9. The correct step should be to add 9 before subtracting 9.

Here is the corrected work:

Step 1: h(x) = (x^2 - 6x + 9) + 7
Step 2: h(x) = (x^2 - 6x + 9) + 7 - 9
Step 3: h(x) = (x^2 - 6x + 9) - 2
Step 4: h(x) = (x - 3)^2 - 2

Now we see that the correct vertex is (3, -2), not (3, 2).