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Typically you have to complete the square, then move the constant term to the left side with your y variable.
I'm assuming you're referring to the quadratic function here and not some other function with a vertex.
can you give me an example becuase its on my test tommorow and my teacher cant explain it
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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)
change the parabola equadion from vertex form to standared form