Question

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

Answer 1

Explanation:

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

`f(x)=-2x^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. `when` `x=2, y=-8`).

`g(x)=2x-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=2x-4`
`2x=4`
`therefore x=2`

y-intercept (when x=0),
`y=2(0)-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: