algebra help, please? a-h-k form?

Question

i can do most of these, but i am stuck on this one.
Convert into a-h-k form by completing the square.
f(x)=x^2-3x+2
your help is greatly appreciated

Answer 1

(-3/2)^2=(-3/2)(-3/2)= 9/4

f(x)= (x^2 -3x +9/4 -9/4) +2

V(9/4)= 3/2 and take the sign in front of the coefficient in front of x

threfore f(x)= (x - 3/2)^2 -9/4 +8/4

and final solution is after simplifying

f(x)= (x-3/2)^2 -(1/4)

Answer 2

Sure, to complete the square, take half of the middle term, and then square it. You want to group it like this:

(x^2 - 3x + 9/4) + 2 - 9/4

Then, when you complete the square, you get

(x - 3/2)^2 - 1/4

So, a is 1, h is + 3/2 and k is -1/4, in the form normally used by math textbooks.

Answer 3

To complete the square of f(x)=x^2-3x+2, divide -3 by 2 to get -3/2 and square this to get 9/4. Add and subtract this.
This makes your quadratic f(x)=x^2-3x+9/4 - 9/4 +2 = (x-3/2)^2 -1/4.
a=1, h= 3/2 , k=-1/4

Answer 4

Say f(x) = ax^2 + bx +c. When you complete the square, you first have to find (1/2b)^2, which in this case is 2.25. You want to make your c-term 2.25, so add .25 to your c-term, and subtract .25 from the other side to keep everything equal.

Now, you can rewrite y = x^2 - 3x +2 as y - 0.25 = x^2 - 3x +2.25

y - 0.25 = (x - 1.5)^2

By the way, h = 1.5 and k = 0.25. You can check by multiplying everything back out... you will get what you started with.

Answer 5

Dunno what a-h-k form is, but you can complete the square like this:
f(x) - 2 + 9/4 = x^2 -3x + 9/4
= (x - 3/2)^2