Question

Standard Form: y = 4x^2 - 12x + 5
Vertex Form?
Intercept Form?

Answer 1

Vertex form :
`y=4(x-(3)/(2))^2-4`

Intercept form :
`y=4(x- (1)/(2)) (x-(5)/(2))`

Explanation:

Here we are given

`y=4x^2-12x+5`

Factoring
`4x^2-12x+5`

We get

`y=4x^2-10x-2x+5=2x(2x-5)-1(2x-5)= (2x-1)(2x-5)`

Factoring 2 from both brackets we get

`y=4(x- (1)/(2)) (x-(5)/(2))`

This is Intercept form

For the vertex form

we have

`h=-(b)/(2a)=- (-12)/(8)= (3)/(2)`

Now substituting in y we get

`k=4((3)/(2))^2-12( (3)/(2))+5=-4[tex]</p><p>The vertex form</p><p>[tex]y=a(x-h)^2+k`

We get

[/tex]y=4(x-\frac{3}{2})^2-4[/tex]