# How do you draw f(x) = -2x^2 and g(x) = 2x-4 on the same graphs?

Oct 4, 2017

#### Explanation:

To draw these on the same graph, you first need to know what each graph looks like individually:

$f \left(x\right) = - 2 {x}^{2}$ is an upside-down parabola:
graph{-2x^2 [-20, 20, -10, 10]}

Due to the $2$ in front of the ${x}^{2}$, the graph is steeper than a usual one. If you are unsure about how to convey the steepness, I recommend you sub in a point on the graph to see where it would be (e.g. $w h e n$ $x = 2 , y = - 8$).

$g \left(x\right) = 2 x - 4$ is a linear equation (i.e. a straight line). This can be graphed by finding the x- and y-intercepts, and then drawing a line that goes through the points.

x-intercept (when y=0),
$0 = 2 x - 4$
$2 x = 4$
$\therefore x = 2$

y-intercept (when x=0),
$y = 2 \left(0\right) - 4$
$\therefore y = - 4$

graph{2x-4 [-40, 40, -20, 20]}

To graph these on the same graph, you need to make sure you have a common scale. These two equations graphed on the same axes look like this: