Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

What is the vertex form of $y = - x^{2} - 2 x + 3$ $y=-x^2-2x+3$ ?

1 Answer

Dec 7, 2015

$y = (- 1) {(x - (- 1))}^{2} + 4$ $y=(-1)(x-(-1))^2+4$

Explanation:

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

Given $y = - x^{2} - 2 x + 3$ $y=-x^2-2x+3$

Extract the $m$ $m$ factor from the terms including an $x$ $x$
$XXX y = (- 1) (x^{2} + 2 x) + 3$ $color(white)("XXX")y= (-1)(x^2+2x) +3$

Complete the square:
$XXX y = (- 1) (x^{2} + 2 x + 1 - 1) + 3$ $color(white)("XXX")y=(-1)(x^2+2x+1-1) +3$

$XXX y = (- 1) (x^{2} + 2 x + 1) + 1 + 3$ $color(white)("XXX")y=(-1)(x^2+2x+1) +1 +3$

$XXX y = (- 1) {(x + 1)}^{2} + 4$ $color(white)("XXX")y=(-1)(x+1)^2 + 4$

$XXX y = (- 1) {(x - (- 1))}^{2} + 4$ $color(white)("XXX")y=(-1)(x-(color(red)(-1)))^2+color(blue)(4)$
which is the graph{-x^2-2x+3 [-6.737, 5.753, -0.565, 5.675]} vertex form with vertex at $(- 1, 4)$ $(color(red)(-1),color(blue)(4))$

Related questions

See all questions in Vertex Form of a Quadratic Equation

Impact of this question

2722 views around the world

You can reuse this answer
Creative Commons License