Question

Hey how do you get from standard form to vertex form?

Answer 1

Explanation:

Conversion of a quadratic equation from standard form to vertex form is done by completing the square method.

Assume the quadratic equation to be $\mathbf{ax^{2}+bx+c=0}$ where x is the variable.

Completing the square method is as follows:

1. send the constant term to other side of equal                 $\mathbf{ax^{2}+bx=-c}$
2. divide the whole equation be coefficient of $\mathbf{x^{2}}$, this will give     $\mathbf{x^{2}+\frac{b}{a}x=- \frac{c}{a}}$
3. add $\mathbf{(\frac{b}{2a})^{2}}$ to both side of equality                                   $\mathbf{x^{2}+2\times\frac{b}{2a}x+\frac{b}{2a}^{2}=-\frac{c}{a}+\frac{b}{2a}^{2}}$
4. Make one fraction on the right side and compress the expression on the left side                                                                          $\mathbf{(x+\frac{b}{2a})^{2}=\frac{b^{2}-4ac}{4a^{2}}}$
5. rearrange the terms will give the vertex form of standard quadratic equation                                                                 $\mathbf{a(x+\frac{b}{2a})^{2}-\frac{b^{2}-4ac}{4a}=0}$

Follow the above procedure will give the vertex form.

(NOTE : you must know that $\mathbf{(x+a)^{2}=x^{2}+2ax+a^{2}}$. Use this equation in transforming the equation from step 3 to step 4)