How do you graph #y=-x^2+4#?

Answer 1

Nathan Axel

As shown below:

The first thing to do is identify what tranformations #x^2# should undergo to reach #-x^2 + 4 #

#-x^2 + 4 # is just #x^2# reflected in the x axis, then translated by #(0,4)# or in words, shifted upward by 4 units

#x^2#: graph{x^2 [-9.625, 10.375, -2.96, 7.04]}

#-x^2# : graph{-x^2 [-9.42, 10.58, -8, 2]}

#-x^2 +4 #: graph{4- x^2 [-9.375, 10.625, -4.32, 5.68]}

Now we can find the intercepts:

#x= 0 => y = 4 #

Passes through #(0,4)#

#y=0 => x^2 = 4 =>x = pm 2 #

Passes thorugh #(pm2,0)#, these our roots.

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Answer 2

Avery Alexander

To graph the equation ( y = -x^2 + 4 ), follow these steps:

Plot the vertex at ( (0, 4) ).
Use the symmetry of the parabola to plot additional points symmetrically on either side of the vertex.
Choose x-values to the left and right of the vertex, and substitute them into the equation to find the corresponding y-values.
Plot these points on the graph.
Draw a smooth curve through the plotted points to represent the parabola.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.