Question

Type the correct answer in the box. Rewrite the quadratic equation in the form $y = a(x - h {)}^{2} + k$$y = 5 {x}^{2} - 30x + 95$

Answer 1

1) To rewrite the quadratic equation y= 5x² -30x +95 into the vertex form we need to find h and k

2) Let's plug into that y=a(x-h)²+k, each variable on the right side. a= 5

$\begin{gathered} h=-\frac{b}{2a}\Rightarrow\frac{-(-30)}{2(5)}=\frac{30}{10}=3 \\ k=\frac{-\Delta}{4a}\Rightarrow\frac{-(b^2-4ac)}{4a}\Rightarrow\frac{-((-30)^2-4(5)(95))}{4(5)}=\frac{1000}{20}=50 \end{gathered}$

3) Hence, we can rewrite y= 5x² -30x +95 as y=5(x-3)²+50