Felicia rewrote a quadratic function in vertex form.
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.
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).