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

1 Answer
Oct 4, 2017

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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:

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