Question

How do you graph the function `f(x)=x^2+2x`?

Answer 1

Refer Explanation section.

Explanation:

y = `x^2` + 2x

It is a quadratic equation
y = `ax^2` + bx + c

Here c = 0 ; hence
y = `x^2` + 2x

Its minimum is at x = `(-b)/(2a)` =`(-2)/(2 xx 1)` = `(-2)/2`= -1

At x = - 1 ; y = `(-1)^2` + (2 (-1)) = 1 - 2 = - 1

At ( -1, -1) the curve turns.

It is upward facing parabola. Its vertex is at ( -1)

Your range of x values must contain this (- 1). Take three values on either side. Calculate their corresponding y values.

Plot the pairs on a graph sheet. Join them all with a smooth curve.

x y
-4 8
-3 3
-2 0
-1 -1
0 0
1 3
2 8

graph{x^2 + 2x [-10, 10, -5, 5]}