Question

How do you find the important points to graph `f(x)=x^2+2x`?

Answer 1

Find the Vertex, X-intercepts, y-intercept

Explanation:

From the given `y=x^2+2x`

the format of `f(x)=y=ax^2+bx+c`

The Vertex `(h, k)`

with `a=1`and `b=2` and `c=0`

`h=-b/(2a)=-2/(2*1)=-1`

`k=c-b^2/(4a)=0-2^2/(4*1)=-4/4=-1`

Vertex `(h, k)=(-1, -1)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The x-intercepts `(x_1, 0)` and `(x_2, 0)`

From the given equation `y=x^2+2x`, set `y=0`,then solve for x values

`0=x^2+2x`
`0=x(x+2)`

then `x_1=0` and `x_2=-2`
The x-intercepts `(x_1, 0)` and `(x_2, 0)` are `(0, 0)`,and `(-2, 0)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The y-intercept `(0, y_1)`

From the given equation `y=x^2+2x`, set `x=0` then solve for the y value

`y=x^2+2x`

`y=0^2+2*(0)`

`y=0` when `x=0`

The y-intercept `(0, y_1)=(0, 0)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I hope the explanation is useful....God bless