How would I convert this quadratic function to intercept and vertex form?

y=4x^2-12x+5

Question

How would I convert this quadratic function to intercept and vertex form?

y=4x^2-12x+5

amistre64 · Answer

by completeing the square

amistre64 · Answer

y = 4x^2 -12x +5 ; regroup

y = (4x^2 -12x) +5 ; factor out a 4

y = 4(x^2 -3x) +5 ; and complete the square ....

this is where knowing the technique is very useful

amistre64 · Answer

y = 4(x^2 -3x+N) +5 -4N ; where N is the value that 
                                            "completes the square"

in this case its 9/4

y = 4(x^2 -3x+9/4) +5 -9 ; compact it

y = 4(x-3/2)^2 - 4

and its done

amistre64 · Answer

given the form:  x^2 +bx;  a complete square is obtained by taking half of "b";  b/2 ... and squareing it:

            (b/2)^2 = b^2/4

amistre64 · Answer

the other trick is in once you add it, you have to subtract it back out in order to keep the same value of the original equation

amistre64 · Answer

x^2 + 3x;   (3/2)^2 = 9/4 ... which is what i meant

anonymous · Answer

Oh, okay...I think I get it a little better now. I always get stuck on completing the square and go downhill from there. Thank you...!

amistre64 · Answer

youre welcome :)