Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you write $f (x) = 3 x^{2} - 24 x + 45$ $f(x)= 3x^2-24x+45$ in vertex form?

1 Answer

Jun 5, 2015

Given $f (x) = 3 x^{2} - 24 x + 45$ $f(x) = 3x^2-24x+45$

Vertex form is
$XXXX$ $color(white)("XXXX")$ $f (x) = {(x - a)}^{2} + b$ $f(x) = (x-a)^2 +b$ with the vertex at $(a, b)$ $(a, b)$

$f (x) = 3 x^{2} - 24 x + 45$ $f(x) = 3x^2-24x+45$
$XXXX$ $color(white)("XXXX")$ $f (x) = 3 (x^{2} - 8 x) + 45$ $f(x) = 3(x^2-8x) +45$ $XXXX$ $color(white)("XXXX")$ extracting the $m$ $m$

$XXXX$ $color(white)("XXXX")$ $f (x) = 3 (x^{2} - 8 x + 16) + 45 - 3 (16)$ $f(x) = 3(x^2-8x+16) + 45 - 3(16)$ $XXXX$ $color(white)("XXXX")$ completing the square

$XXXX$ $color(white)("XXXX")$ $f (x) = 3 {(x - 4)}^{2} - 3$ $f(x) = 3(x-4)^2 -3$ $XXXX$ $color(white)("XXXX")$ vertex form

Related questions

See all questions in Vertex Form of a Quadratic Equation

Impact of this question

8840 views around the world

You can reuse this answer
Creative Commons License