Question

Write the equation of the parabola in vertex form.vertex (3,1), point (2,-2)f(x) =

Answer 1

rom the point it passed We were given

Vertex = (3,1)

Point = (2, -2)

The equation of the parabola is given by:

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

where (h, k) is the vertex = (3,1)

a is a cnstant

On substitution:

`y=a(x-3)^2+1`

Substituting the value of (x,y) from the point it passed through to find a:

`\begin{gathered} y=a(x-3)^(2)+1 \\ \\ -2=a(2-3)^2+1 \\ \\ -2=a+1 \\ \\ a=-3 \end{gathered}`

Therefore substitute a into the original equation:

`y=-3(x-3)^2+1`

The equation of the parabola is given by:

y = -3(x-3)^2 + 1