Question

A parabola opening up or down has vertex (0,6) and passes through (-8, -10) Write its equation in vertex form.

Answer 1

The vertex form of a parabola is:

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

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

Substituting with (0, 6) as the vertex, we get:

`\begin{gathered} y=a(x-0)^2+6 \\ y=ax^2+6 \end{gathered}`

Substituting with the point (-8, -10), we can find a, as follows:

`\begin{gathered} -10=a(-8)^2+6 \\ -10=a\cdot64^{}+6 \\ -10-6=a\cdot64 \\ (-16)/(64)=a \\ -(1)/(4)=a \end{gathered}`

Therefore, the equation is:

`y=-(1)/(4)x^2+6`