Question

A parabola opening up or down has vertex (0, 0) and passes through (12, 18). Write its equation in

vertex form.
Simplify any fractions.

Answer 1

`y=(1)/(8)x^2`

Explanation:

`\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}`

Given that the vertex of the parabola is (0, 0):

• h = 0
• k = 0

Substitute the values of h and k into the formula:

`y=a(x-0)^2+0`

`y=ax^2`

Given that the parabola passes through the point (12, 18), substitute this into the equation and solve for a:

`18=a(12)^2`

`18=144a`

`a=(18)/(144)`

`a=(1)/(8)`

Therefore, the equation of the parabola in vertex form is:

`y=(1)/(8)x^2`