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

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

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