Question

How do you write the quadratic in vertex form given `y=5x^2+5x-3`?

Answer 1

To be in vertex form a quadratic needs to be expressed as
`y=color(red)(m)(x-color(green)(a))^2+color(orange)(b)`
(where `(a,b)` is the vertex of the quadratic),

`y=5x^2+5x-3`

`y = color(red)(5)(x^2+x)-3 " extract the "color(red)( m)" term"`

`y = color(red)(5)(color(blue)(x^2+x+(1/2)^2) -(1/2)^2)-3 " "color(blue)("complete the square")`

`y=color(red)5(x+1/2)^2 - 5/4 -3`

`y=color(red)(5)(x- color(green)( (-1/2)))^2 + color(orange)(( -4 1/4))`