**Given information**:

The quadratic equation y=0.01x3−x2+5 .

**Graph**:

The graph of the quadratic equation y=0.01x3−x2+5 can be sketched in the cartesian plane,

Consider the quadratic equation, y=0.01x3−x2+5 .

Now put the values of x in the equation to find the values of y or to find the real roots of y with the help of x .

Rewrite the equation take common:

y=0.01x3−x2+5y=0.01(x3−100x2+500)

Now substitute the value of y in equation y=0.01(x3−100x2+500) .

y=0.01(x3−100x2+500)0=0.01(x3−100x2+500)0=(x3−100x2+500)

Eliminate the quadratic term by substituting:

y=x+1003x=y−

y=x+1003x=y−1003

Now put the value of x in the equation, (x3−100x2+500)=0 .

(x3−100x2+500)=0(y−1003)3−100(y−1003)2+500=0

The value of x -intercepts are:

x≈2.21174271x≈~2.2617928

Substitute the value x=0 in the equation y=0.01x3−x2+5 :

y=0.01x3−x2+5y=0.01(0)3−02+5y=5

Substitute the value x=1 in the equation y=0.01x3−x2+5 :

y=0.01x3−x2+5y=0.01(1)3−12+5y=0.01−1+5y=4.01

Substitute the value x=2 in the equation y=0.01x3−x2+5 :

y=0.01x3−x2+5y=0.01(2)3−22+5y=0.01⋅8−4+5y=1.08

Substitute the value x=−1 in the equation y=0.01x3−x2+5 :

y=0.01x3−x2+5y=0.01(−1)3−(−1)2+5y=−0.01+1+5y=5.99

Substitute the value x=−2 in the equation y=0.01x3−x2+5 :

y=0.01x3−x2+5y=0.01(−2)3−(−2)2+5y=0.01⋅8+4+5y=9.08

Observed that when the value of x increases then the value of y decreases slightly.

When the value of x decreases then the value of y increases slightly.

Steps to plot the graph of the equation y=0.01x3−x2+5 with the help of graphing utility are as follows:

Step 1: Press MODE key.

Step 2: Use the down arrow key to reach FUNC option.

Step 3: Press ENTER key.

Step 4: Press Y= key.

Step 5: Enter the function 0.01x3−x2+5 .

Step 6: Press WINDOW key. Change the settings to

Xmin=−10Xmax=10Ymin=−10Ymax=10

For better view of graph.

Step 8: Press GRAPH key.

The result obtained on the screen is provided below,

**Interpretation**:

The equation of the function y=0.01x3−x2+5 represents a parabola.

The parabola opens downwards.

The x− intercepts are the points on x−axis where the graph of the equation touches x−axis .

At x -axis y is always zero.

Recall that the graphical approach to solve the equation simultaneously.

Therefore, in the equation, y=0.01x3−x2+5 there is no x− intercepts.

Therefore, the equation y=0.01x3−x2+5 is symmetric about the y− axis Initially the graph of the function y=0.01x3−x2+5 increases when increase the value of x ,the graph is a parabola shaped graph.