Question

What is the vertex form of `x= 10y^2-31y+15`?

Answer 1

The vertex form for a parabola is a function of the form;

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

Where `(h,k)` is the vertex of the parabola. To convert a quadratic to vertex form, we want to start by isolating the `y` terms and completing the square.

`x=10(y^2-31/10 y)+ 15`

Complete the square inside the parenthesis.

`x=10(y^2-31/10 y + 961/400 - 961/400) + 15`

`x=10(y^2-31/10 y + 961/400) - 961/40 + 15`

`x=10(y^2-31/20)^2 - 24 1/400 + 15`

`x=10(y^2-31/20)^2 - 9 1/400`

This is the vertex form of the equation.