# How do I change y = 9x^2 + 3x - 10 into vertex form?I am looking to rewrite this equation into the the vertex form y=a(x-h)^2+k, where a is the leading coefficient and (h,k) is the vertex. I...

How do I change y = 9x^2 + 3x - 10 into vertex form?

I am looking to rewrite this equation into the the vertex form y=a(x-h)^2+k, where a is the leading coefficient and (h,k) is the vertex. I understand to start by rewriting the formula and then completing the square, but then the answers I get when I plug them into the formula, never have the same graph as the original.

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Expert Answers

justaguide | Certified Educator

The equation y = 9x^2 + 3x - 10 has to be converted into the vertex form y = a(x-h)^2 + k

y = 9x^2 + 3x - 10

=> y =9(x^2 + x/3 - 10/9)

=> y = 9(x^2 + (2*x)/(3*2) + 1/36 - 1/36 - 10/9)

=> y = 9((x + 1/6)^2 - 41/36)

=> y = 9(x + 1/6)^2 - 41/4

**The required vertex form of y = 9x^2 + 3x - 10 is y = 9(x + 1/6)^2 - 41/4**