What is the vertex form of y= 9x^2 + 2x + 2/7 ?

1 Answer
Feb 26, 2018

See below:

Explanation:

The vertex form of a quadratic equation is

y=a(x-h)^2+k with (h,k) as the vertex.

To find the vertex form of a quadratic equation, complete the square:

y=9(x^2+2/9x+(1/9)^2-(1/9)^2)+2/7

y=9(x+1/9)^2-9/81+2/7

y=9(x+1/9)^2+11/63

The vertex is (-1/9,11/63)

You can also find the vertex with formulas:

h=-b/(2a)

k=c-b^2/(4a)

------------

h=-2/(2*9)=-1/9

k=2/7-(-2)^2/(4*9)=2/7-4/36=11/63

so the vertex is at

(-1/9,11/63)

You can also find vertex form this way:

y=a(x+1/9)+11/63

Plug in a from the original equation:

y=9(x+1/9)+11/63

Apologies for the length :)