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

Aug 3, 2018

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Explanation:

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

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

$y = f \left(x\right) = {x}^{2}$

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

Make a data table for the given function

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

The graph of the given function

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

is compressed horizontally since $a = - 4$