Compare the Graph

g(x)=-\frac{1x^2}{5}-2 \\ with\\y=x^2

Step By Step Solution:

Calculate a few values of the function

g(x)=-\frac{1}{5}x^{2}-2

So,calculate the value of g(x) at x=-10:

g(-10)=-\frac{1}{5}(-10)^{2}-2 \\\therefore g(-10)=-22

Using the same procedure, calculate the value of g(x) for x=-5, x=0, x=5, and x=10.

{g(x)=-\frac{1}{5}x^{2}-2} 

through the plotted points.

y=x^{2}

into the same coordinate plane.

Notice that the axis of symmetry for both graphs is line x=0.

The graph of the function

y=x^{2}

opens upward and the graph of function

g(x)=-\frac{1}{5}x^{2}-2

opens downward.

g(x)=-\frac{1}{5}x^{2}-2

is wider than the graph of function

y=x^{2}

The vertex of the function

g(x)=-\frac{1}{5}x^{2}-2

is 2 units lower than the vertex of function

 y=x^{2}

Solution:

g(x)=-\frac{1}{5}x^{2}-2

is shown.

The graph has the same axis of symmetry as the graph of function

{y=x^{2}} 

but it opens downward, it is wider and the vertex is lower for 2 units.

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