Answer:
Vertex form : [tex]y=4(x-\frac{3}{2})^2-4[/tex]
Intercept form : [tex]y=4(x- \frac{1}{2}) (x-\frac{5}{2})[/tex]
Step-by-step explanation:
Here we are given
[tex]y=4x^2-12x+5[/tex]
Factoring [tex]4x^2-12x+5[/tex]
We get
[tex]y=4x^2-10x-2x+5=2x(2x-5)-1(2x-5)= (2x-1)(2x-5)[/tex]
Factoring 2 from both brackets we get
[tex]y=4(x- \frac{1}{2}) (x-\frac{5}{2})[/tex]
This is Intercept form
For the vertex form
we have
[tex]h=-\frac{b}{2a}=- \frac{-12}{8}= \frac{3}{2}[/tex]
Now substituting in y we get
[tex]k=4(\frac{3}{2})^2-12( \frac{3}{2})+5=-4[tex]
The vertex form
[tex]y=a(x-h)^2+k[/tex]
We get
[/tex]y=4(x-\frac{3}{2})^2-4[/tex]
