What is the vertex form of $4 y = x (x + 12) + 13$ $4y = x(x+12)+13$ ?

Question

What is the vertex form of $4 y = x (x + 12) + 13$ $4y = x(x+12)+13$ ?

1 Answer

Impact of this question

1462 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-25T12:15:04

$y = \frac{1}{4} {(x - (- 6))}^{2} + (- 6)$ $y=1/4(x-(-6))^2+(-6)$
$XXXXXXXXXXX$ $color(white)("XXXXXXXXXXX")$ with vertex at $(- 6, - 6)$ $(-6,-6)$

Explanation:

The general vertex form is
$XXX y = m {(x - a)}^{2} + b$ $color(white)("XXX")y=m(x-a)^2+b$
with vertex at $(a, b)$ $(a,b)$

Given:
$XXX 4 y = x (x + 12) + 13$ $color(white)("XXX")4y=x(x+12)+13$
Expand the right side
$XXX 4 y = x^{2} + 12 x + 13$ $color(white)("XXX")4y=x^2+12x+13$
Complete the square
$XXX 4 y = x^{2} + 12 x + 6^{2} + 13 - 36$ $color(white)("XXX")4y=x^2+12xcolor(green)(+6^2)+13color(green)(-36)$
Rewrite as a squared binomial (and combine the constant)
$XXX 4 y = {(x + 6)}^{2} - 24$ $color(white)("XXX")4y=(x+6)^2-24$
Divide both sides by $4$ $4$
$XXX y = \frac{1}{4} {(x - (- 6))}^{2} + (- 6)$ $color(white)("XXX")y=1/4(x-(-6))^2+(-6)$

Science

Math

Humanities

... and beyond

What is the vertex form of $4 y = x (x + 12) + 13$ $4y = x(x+12)+13$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the vertex form of 4y=x(x+12)+13 4y = x(x+12)+13 ?

1 Answer

Explanation:

Related questions

Impact of this question

What is the vertex form of $4 y = x (x + 12) + 13$ $4y = x(x+12)+13$ ?