Cole rewrote a quadratic function in vertex form.

Question

h(x)= x^2−6x+7

Step 1: h(x)= (x^2−6x+ )+7

Step 2: h(x)=(x^2−6x+ 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. step by step

Answer 1

Cole is incorrect. The mistake is in Step 2 where he added 9 inside the parentheses without subtracting it outside of the parentheses.

Corrected steps:

Step 1: h(x)= (x^2−6x+ )+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 + 5

Therefore, the correct vertex is (3, 5).