Compare the Graph

Compare the Graph of two functions
Compare the graph of g(x) with the graph of y
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.

Table: For Value of g(x) at different value of x
Table: For Value of g(x) at different value of x
Plot the Graph
Plot the points (-10,-22),(-5,-7),(0,-2),(5,-7),(10,-22)
Graph of the function
Graph of the function
{g(x)=-\frac{1}{5}x^{2}-2} 

through the plotted points.

Graph the function of y =x^2
Graph the function
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

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.

The graph of the function
The graph of the function
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:

The graph of the function
The graph of the function
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.

Similar post

Solve the inequality and graph.

Evaluate the value of the given series.

Given rhombus FGHI below, Solve for x.

Spread the love

Leave a Comment