How do you identify the important parts of #y= -4x^2# to graph it?

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Answer 1 · 2018-08-03T05:02:05

#" "#
Please read the explanation.

#" "#
Vertex-Form of a Quadratic Equation:

#color(red)(y=f(x)=a(x-h)^2+k#, where

#color(red)((h,k)# is the Vertex

#y=f(x)=x^2#

is the parent function

We can see that #a=1; h=0,k=0#

Vertex #color(red)((0,0)#

Axis of Symmetry is at #color(red)((x=0)#

Since #a>0#, the parabola opens up.

For the given function:

#color(blue)(y=f(x)=-4x^2#

#a=-4, h=0, k-0#

The value of #color(red)(a, (a<0)#, the parabola opens down.

Vertex is at #color(red)((0,0)#

Axis of Symmetry is at #color(red)((x=0)#

Make a data table for the parent function

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Make a data table for the given function

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Draw the graphs for both of them and analyze the behavior of the quadratic functions:

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The graph of the given function

#color(blue)(y=f(x)=-4x^2#

is compressed horizontally since #a=-4#

Hope this is helpful;.