### Home > CCA2 > Chapter 6 > Lesson 6.1.5 > Problem6-84

6-84.

On their Team Assessment, Raymond, Sarah, Hannah, and Aidan were given $y=4x^2−24x+7$ to change into graphing form. Raymond noticed that the leading coefficient was a $4$ and not a $1$. His team agreed on a way to start rewriting, but then they worked in pairs and got two different solutions, shown below.

Raymond and Hannah

(1)  $y=4x^2−24x+7$
(2)  $y=4(x^2−6x)+7$
(3)  $y=4(x^2−6x+3^2)+7−36$
(4) $y=4(x−3)^2−29$

Aidan and Sarah

(1)  $y=4x^2−24x+7$
(2)  $y=4(x^2−6x+9)+7−9$
(3)  $y=4(x−3)^2+7−3^2$
(4)  $y=4(x−3)^2−2$

Hannah says, “Aidan and Sarah made a mistake in Step 3. Because of the factored 4 they really added 4(9) to complete the square, so they should subtract 36, not just 9." Is Hannah correct? Justify your answer by showing whether the results are equivalent to the original equation.