Question

What is the vertex form of `y=5x^2+17x+13` ?

Answer 1

When given an equation of the form:

`y=ax^2+bx+c`

The vertex form is:

`y=a(x-h)^2+k`

where `h = -b/(2a) and k = ah^2+bh+c`

Explanation:

Given:

`y=5x^2+17x+13`

Please observe that `a = 5, b = 17, and c = 13`

Substitute 5 for a in the vertex form:

`y = 5(x-h)^2+k`

Compute the value of h:

`h = -17/(2(5))`

`h = -17/10`

Substitute the value of h into the vertex form:

`y = 5(x-(-17/10))^2+k`

Compute the value of k:

`k = 5(-17/10)^2+17(-17/10)+13`

`k = -29/20`

Substitute the value of k into the vertex form:

`y = 5(x-(-17/10))^2+ (-29/20)`

The above equation is the vertex form.