What is the vertex form of $y= x(x+3)$ ?

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Answer 1 · 2015-12-13T19:58:48

$(-3/2,-9/4)$

Distribute the $x$ .

$y=x^2+3x$

This is in the $ax^2+bx+c$ form of a parabola where

$a=1,b=3,c=0$

The vertex formula of a quadratic equation is

$(-b/(2a),f(-b/(2a)))$

The $x$ -coordinate is

$-b/(2a)=-3/(2(1))=-3/2$

The $y$ -coordinate is

$f(-3/2)=-3/2(-3/2+3)=-3/2(-3/2+6/2)=-9/4$

Thus, the vertex is $(-3/2,-9/4)$ .

graph{x(x+3) [-10, 10, -5, 5]}

Indeed, the vertex is located at the point $(-1.5,-2.25)$ .

What is the vertex form of y= x(x+3) y= x(x+3) ?