Q:

How to convert from standard form to vertex form

Accepted Solution

A:
ANSWERSee explanationEXPLANATIONThe standard form of a quadratic equation is:[tex]y = a {x}^{2} + bx + c[/tex]To convert this function to standard form, you follow the steps below:Factor 'a' from the variable termsAdd and subtract the square of half the coefficient of x.Factor the perfect squaresSimplify the constant terms to get the vertex form as [tex]y = a {(x - h)}^{2} + k[/tex]For example:Given the standard form:[tex]y = 2 {x}^{2} + 12x + 10[/tex]Factor 2 from the variable terms[tex]y = 2 {(x}^{2} + 6x) + 10[/tex]Add and subtract the square of 3.[tex]y = 2 {(x}^{2} + 6x + 9 - 9) + 10[/tex][tex]y = 2 {(x}^{2} + 6x + 9) + 2( - 9) + 10[/tex]Factor the perfect square an simplify[tex]y = 2 ({x + 3)}^{2} - 8[/tex]This is the vertex form