Convert From General to Standard Form

dinahspence

Hey everyone, I was wondering if you could help me with something.

Can someone give me the step to convert the two equations from general to standard form? If you could, it would be such a great help to me. Thanks

y= x^2 - 2X + 5 and y= -3x^2 + 12x -4

Mark44

It's been quite a few years, so I don't recall what standard form looks like. Is it like this?
y = A(x - h)² + k

If so, what you need to do is complete the square in your x terms. For example, if your equation was y = -2x² - 4x + 7, you would do this.

y = -2x² - 4x + 7

Factor -2 from each of the x terms, getting this:
y = -2(x² + 2x) + 7

Complete the square inside the parentheses, keeping track of what you really added.
y = -2(x² + 2x + 1) + 7 + 2

In the step above, it looks like I added 1, but I really added -2, so to keep the right side equal to what it was, I have to balance that by adding + 2.

y = -2(x + 1)² + 9

Not sure if this is the form you're looking for, but it is very useful nevertheless. Here we have the equation of a parabola whose vertex is located at (-1, 9).

If this is the form you're looking for, apply the same technique to your problems.

dinahspence

thanks!
can anyone help me with the second one?

symbolipoint

The second one would be easier if you factor into -3 and the appropriate quadratic polynomial.

y= -3x^2 + 12x -4 = -3(x^2 - (-4)x + (4/3))

Now you want to focus most of your attention to completing the square for the polynomial, and then clean the remaining steps.