Question

What is the vertex form of #y=5x^2 + 4x - 3?

Answer 1

`y=5(x+2/5)^2-19/5`

Explanation:

A parabola has the form:
`y=ax^2+bx+c`
`y=5x^2+4x-3`

The vertex form of a parabola is:
`y=a(x-h)^2+k`

To find the vertex `(h,k)` of a parabola we use:

`h =-b/{2a}=-4/{2*5}=-4/10=-2/5=-0.4`

And to find the y coordinate we just evaluate in the original function with the value we just found:

`k=f(-2/5)=5(-2/5)^2+4(-2/5)-3=-3.8`

The vertex is `(-0.4,-3.8)`. Rewriting the equation using the vertex form, we have:

`y=5(x-(-0.4))^2+(-3.8)`
`y=5(x+0.4)^2-3.8`

If you want to have it in a nicer way:

`y=5(x+2/5)^2-19/5`

graph{5(x+2/5)^2-19/5 [-10, 10, -5, 5]}
Click on the graph to see its vertex