First of all, why don't we just get the answer? Graph it! I use desmos. Just reading the graph it looks like the answer is
y = 2(x - 8) - 72 so let's see if we can get it. By the way, I'm a great believer in graphs.
Step One
Isolate the first two terms. That just means put brackets around those first 2 terms.
y = (2x^2 - 32x ) + 56
Step Two
Take out the common factor of 2.
y = 2(x^2 - 16x) + 56 So far the 56 is unaffected.
Step Three.
Add 64 inside the brackets. I'm going to explain this as carefully as I know how, but you'll have to read it a couple of times to get it clear.
Start by dividing the linear term ( -16x -- remember that from yesterday?) by 2. That gives you 8 [drop the x].
Now square it. that gives you 64. So far the equation is
y = 2(x^2 - 16x + 64)+56
Step Four
Because you added 64 inside the brackets, you have to compensate what you've done. The equation is no longer balanced to what you started out with. So the 56 is finally going to be affected.
2* 64 is what you have added in total. So that has to be subtracted after the 56
The equation now looks like this.
y = 2(x^2 - 16x + 64)+56 - 128
combine the 56 - 128 into one term
y = 2(x^2 - 16x + 64) - 72
Step 5
Represent what's inside the brackets as a perfect square.
y = 2(x - 8)^2 - 72
Step 6
The boxes in the question are 2 -8 and - 72
Here's a nifty thing to know. The x coordinate is 1/2 the distance between the roots. So it's 1/2(2 + 14) = 8. Or you can just look inside the brackets and read what it would take to make it zero.
x - 8 = 0
x = 8
Both methods work.
2 - 8 - 72
8 <<<<<< are what goes inside the boxes.
