how do you change standard form into vertex form

Question

anonymous · Answer

Typically you have to complete the square, then move the constant term to the left side with your y variable.

anonymous · Answer

I'm assuming you're referring to the quadratic function here and not some other function with a vertex.

anonymous · Answer

can you give me an example becuase its on my test tommorow and my teacher cant explain it

anonymous · Answer

So lets say you have some quadratic equation in the form:
$$y = x^2 + 2x -8$$

To write it in vertex form, we need to have something like:
$$y-y_1 = C(x-x_1)^2$$

So we need to take the x^2 and the 2x and make something that is just (x-x1)^2. To do that, we take half of the coefficient on the x term and square that. So half of 2 is 1, 1 squared is 1.

Then we simultaneously add and subtract (adding a 0) that amount out of the equation:

$$\implies y = x^2 + 2x + 1 - 1\ - 8$$
Then we collect out completed square:
$$\implies y =(x-1)^2 - 1 -8$$
Combine the constant parts:
$$\implies y = (x-1)^2 - 9$$

Then add or subtract the constant part to the other side:
$$\implies y+9 = (x-1)^2$$

That's vertex form and shows that the quadratic has a vertex at (1,-9)

anonymous · Answer

change the parabola equadion from vertex form to standared form

anonymous · Answer

i think that  it because i suck and math

anonymous · Answer

ok so if the equation is: $$3x ^{2} + 4x - 7$$