
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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