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

1 Answer
Feb 1, 2016

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.