Question

-8 1-6N-х68-685.Use vertex form to write the equation of the parabola.y=3(2-2) - 2y = 3(x+2) +2y = (x+2) +2y=3(x-2) +2

Answer 1

The vertex form of a parabola is:

$y=a(x-h)^2+k$

where (h,k) is the vertex and a is some constant.

From the graph, the vertex is located at (-2, 2), that is, h = -2 and k = 2. Substituting into the equation, we get:

$\begin{gathered} y=a(x-(-2))^2+2 \\ y=a(x+2)^2+2 \end{gathered}$

Also, the point (-1, 5) is on the parabola, then:

$\begin{gathered} 5=a(-1+2)^2+2 \\ 5=a\cdot1+2 \\ 5-2=a \\ 3=a \end{gathered}$

Finally, the equation is:

$y=3(x+2)^2+2$