Question

What is the vertex form of `y= 5x^2 + 9x − 4`?

Answer 1

`y=5(x+9/10)^2-161/20`

Explanation:

Vertex form of equation for `y=ax^2+bx+c` is `y=a(x-h)^2+k` and vertex is `(h,k)`.

As `y=5x^2+9x-4`, we have

`y=5(x^2+9/5x)-4`

= `5(x^2+2xx9/10x+(9/10)^2-(9/10)^2)-4`

= `5((x+9/10)^2-5*(9/10)^2-4`

= `5(x+9/10)^2-81/20-4`

= `5(x+9/10)^2-161/20`

and as such vertex is `(-9/10,-161/20)` or `(-9/10,-8 1/10)`

graph{5x^2+9x-4 [-3.54, 1.46, -8.43, -5.93]}