How do you factor #y = 4 (x - 4)^2 + 4# I have been working on this for days and I can’t find the answer. Can anybody help me???
There are a number of possible ways, but I've shared the way I'd do it below. In the end I didn't get a solution, though...
It's a toughie, and (for me at least) factoring always involves some trial and error. In the end I worked through the process with one guess that didn't work out, but hopefully that sets you up well to find the solution.
Here's how I'd approach it:
First expand the square:
Now multiply through with
A starting guess for the factors might be:
Why do I use minus signs both terms? Because the middle term of the quadratic is negative by the final term is positive.
We know that:
The tricky bit is that factor of
(expand the brackets to see why this is the case)
Now we have two equations in two unknowns, so we use our toolkit for simultaneous equations.
Substituting this value into the other equation:
Multiply through by
Which is a quadratic, so now we need our quadratic tools. I tend to use the quadratic formula:
If we substitute both values back into
Hmm, these fractional factors suggest to me that perhaps that first guess should have been:
Nope: when I tried that and ran it through I get the square root of a negative number. We can deal with 'unreal roots', but probably not here.
I don't have the time or space here to go through the whole process again, so I'll leave it to you to work through it...
For me it is easy. See reasoning below
We know that
Hope this help