Question

Express the equation y=x^2+6+19 in the form y=a(x-h)^2 then identify a, h , kA=H=K=

Answer 1

a = 1

h = -3

k = 10

Explanation:

We have the following equation:

`y=x^2+6x+19`

We convert the equation to its vertex form, like this:

`\begin{gathered} y=a\left(x-h\right)^2+k \\ \\ y=x^2+6x+19+3^2-3^2 \\ \\ y=x^2+6x+3^2+19-3^2 \\ \\ x^2+6x+3^2=\left(x+3\right)^2 \\ \\ y=\left(x+3\right)^2+19-9 \\ \\ y=\left(x+3\right)^2+10 \\ \\ y=\left(x-\left(-3\right)\right)^2+10 \\ \\ \text{ Therefore:} \\ \\ a=1 \\ \\ h=-3 \\ \\ k=10 \end{gathered}`