Question

I'm having trouble with Completing the Square in Algebra II... Can someone help me? I have a few practice problems I need help understanding. I'll be posting the problems shortly.

Answer 1

You must show your work on each of the following questions.

Answer 2

Ok so completing the square is pretty simple for the x^2+24x+90=0 do you know how we would start that off?

Answer 3

isolate the x variables

Answer 4

oh wait... Wouldn't we factor?

Answer 5

nope you got it right isolate the values

Answer 6

then take the middle value divide it by 2 then double it (multiply by 2) and square root it and then the solution will be +/-

Answer 7

its difficult to explain but i hope you get it

Answer 8

@amistre64 can you help me?

Answer 9

in COMPLETING THE SQUARE method you just add the "SQUARE OF THE HALF OF THE COEFFICIENT OF THE LINEAR TERM I.E. TERM WITH SINGLE X"

Answer 10

Okay... Can you help with the first one?

Answer 11

which one??

Answer 12

The first one in the picture I posted.

Answer 13

I assume here that by General Form you mean the Standard Form i.e. f(x) = a(x-h)² + k

Since the quadratic is already in general form of f(x)= ax² + bx + c.

y = 3x² - 24x + 10
y = 3(x² - 8x) + 10

Now inside the bracket the coefficient of the linear term i.e. 8x is 8
Also half of 8 is 4
So we add as well as subtract square of 4 as below

y = 3(x² - 8x + (4)² - (4)² ) + 10
y = 3(x² - 8x + 16 - 16) + 10
y = 3(x² - 8x + 16) - 48 + 10

But (x² - 8x + 16) = (x - 4)²
So,
y = 3((x - 4)² ) - 48 + 10
y = 3(x - 4)² - 38