Question

How to change from standard for to vertex form

Answer 1

If the equation is y = 3(x + 4)2 - 6, the value of h is -4, and k is -6. To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a(x - h)2+ k, you use the process of completing the square. Let's see an example. Convert y = 2x2 - 4x + 5 into vertex form, and state the vertex.

Answer 2

Standard form is
ax^2+bx+c=y
to change to vertex form
complete the square

HOW TO COMPLETE THE SQUARE
first, isolate the x terms
(ax^2+bx)+c=y
factor out a
a(x^2+(b/a)x)+c=y
take 1/2 of the coefient of the x term and square it
(b/a) time 1/2=b/(2a), square it, $\frac{b^2}{4a^2}$
now add positive and negative inside parenthasees
a(x^2+(b/a)x+$\frac{b^2}{4a^2}$-$\frac{b^2}{4a^2}$)+c=y
factor perfect square
a(($(x+ \frac{b^2}{4a^2})^2$-a$\frac{b^2}{4a^2}$)+c=y
distribute
$a(x+ \frac{b^2}{4a^2})^2 -a \frac{b^2}{4a^2}+c=y$
 $a(x+ \frac{b^2}{4a^2})^2 - \frac{b^2}{4a}+c=y$
that is vertex form and how to complete the square

for ax^2+bx+c=y
vertex form is
 $a(x+ \frac{b^2}{4a^2})^2 - \frac{b^2}{4a}+c=y$