Respuesta :
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 [tex]\mathbf{ax^{2}+bx+c=0}[/tex] where x is the variable.
Completing the square method is as follows:
- send the constant term to other side of equal [tex]\mathbf{ax^{2}+bx=-c}[/tex]
- divide the whole equation be coefficient of [tex]\mathbf{x^{2}}[/tex], this will give [tex]\mathbf{x^{2}+\frac{b}{a}x=- \frac{c}{a}}[/tex]
- add [tex]\mathbf{(\frac{b}{2a})^{2}}[/tex] to both side of equality [tex]\mathbf{x^{2}+2\times\frac{b}{2a}x+\frac{b}{2a}^{2}=-\frac{c}{a}+\frac{b}{2a}^{2}}[/tex]
- Make one fraction on the right side and compress the expression on the left side [tex]\mathbf{(x+\frac{b}{2a})^{2}=\frac{b^{2}-4ac}{4a^{2}}}[/tex]
- rearrange the terms will give the vertex form of standard quadratic equation [tex]\mathbf{a(x+\frac{b}{2a})^{2}-\frac{b^{2}-4ac}{4a}=0}[/tex]
Follow the above procedure will give the vertex form.
(NOTE : you must know that [tex]\mathbf{(x+a)^{2}=x^{2}+2ax+a^{2}}[/tex]. Use this equation in transforming the equation from step 3 to step 4)
