Question

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

Answer 1

Step-by-step 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)+(b)/(a)x=- (c)/(a)}`
3. add
   `\mathbf{((b)/(2a))^(2)}` to both side of equality
   `\mathbf{x^(2)+2*(b)/(2a)x+(b)/(2a)^(2)=-(c)/(a)+(b)/(2a)^(2)}`
4. Make one fraction on the right side and compress the expression on the left side
   `\mathbf{(x+(b)/(2a))^(2)=(b^(2)-4ac)/(4a^(2))}`
5. rearrange the terms will give the vertex form of standard quadratic equation
   `\mathbf{a(x+(b)/(2a))^(2)-(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)