Verified answer

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

y = 3 + 4(x+3)^2

y = 4x^2 + 24x + 39

First, you have to identify "standard" form. The general form of a quadratic, or 2nd order, equation is:

ax² + bxy + cy² + dx + ey + f = 0

If that's the form you're looking for, expand the equation to separate the terms so that they match the desired form of the equation:

y-3 = 4(x+3)²

y-3 = 4(x²+6x + 9)

y-3 = 4x²+24x+36

and the general form of the equation is:

4x² + 24x - y + 39 = 0

with:

a = 4

b = 0

c = 0

d = 24

e = -1

f = 39

The equation is also the equation of a parabola which can be written in standard "vertex" form as:

y = 4(x+3)² + 3

So, what is the "standard" form you're searching for?

1/4(y-3) = (x+3)^2

y = 4 ( x + 3 ) ² + 3 is the answer.

If desired :-

y = 4 ( x ² + 6 x + 9 ) + 3

y = 4 x ² + 24 x + 39

The given one is a second degree expression for x and first degree for y; so this represents a parabola with its axis parallel to y-axis, that is called vertical axis symmetry parabola;

The standard form for this is: (x - h)^2 = 4a(y - k)

Hence the standard form for this is: {x - (-3)}^2 = (1/4)(y - 3)

Another standard form is axis, parallel to x-axis, which is called a horizontal axis of symmetry;

here the standard form is: (y - k)^2 = 4a(x - h)

y = 4(x+3)^2 + 3

that's all you have to do.

you can do more by simplifying, but this is an acceptable answer.

This is how wolframalpha.com did it.

http://www.wolframalpha.com/input/?i=y+-+3+%3D+4(x...

Well, first off, isn't the standard form ax+by=c?

If it is, then I believe the answer is:

4x^2 + (-y) = -27

If it isn't... then don't listen to me. =)

y-3=4(x²+6x+9)

y-3=4x²+24x+36

y=4x²+24x+39

look in the back of the book or on google