Question

How do you identify the important parts of `y= x^2+2x` to graph it?

Answer 1

y:intercept: `0`
x-intercepts: `0` and `-2`
vertex at: `(-1,-1)`

Explanation:

The y-intercept is the value of `y` when `x=0`
`color(white)("XXX")y=0^2+2(0)=0`

The x-intercepts are the values of `x` when `y=0`
`color(white)("XXX")0=x^2+2x=(x)(x+2)`
`color(white)("XXX")x=0` or `x=-2`

Convert `y=x^2+2x` into vertex form:
`color(white)("XXX")y=(x^2+2x+1)-1`
`color(white)("XXX")y=(x+1)^2-1`
`color(white)("XXX")y=(x-(color(red)(-1)))^2+(color(blue)(-1))`
which is the vertex form of the equation with the vertex at `(color(red)((-1)),color(blue)((-1)))`