Chapter 1.9, Problem 12E

To determine

To graph: The function $y=-100x^2$ in a graphing window.

Explanation of Solution

Given information:

The equation of the function $y=-100x^2$ .

Graph:

The graph of the function $y=-100x^2$ .

Substitute $x=0$ , in the equation $y=-100x^2$ ,

  $\begin{array}{l}y=-100x^2\\ y=0\end{array}$

Substitute $x=1$ , in the equation $y=-100x^2$ ,

  $\begin{array}{l}y=-100x^2\\ y=-100{\left(1\right)}^2\\ y=-100\end{array}$

Substitute $x=2$ , in the equation $y=-100x^2$ ,

  $\begin{array}{c}y=-100x^2\\ y=-100{\left(2\right)}^2\\ y=-100\left(4\right)\\ y=-400\end{array}$

Observe that as the value of $x$ increases there is the huge increment in value of $y$ .

Steps to plot the graph of the equation $y=-100x^2$ with the help of graphing utility are as follows:

Step 1: Press $\boxed{\text{MODE}}$ key.

Step 2: Use the down arrow key to reach $\boxed{\text{FUNC}}$ option.

Step 3: Press $\boxed{\text{ENTER}}$ key.

Step 4: Press $\boxed{\text{Y=}}$ key.

Step 5: Enter the function $-100x^2$ .

Step 6: Press $\boxed{\text{WINDOW}}$ key. Change the settings to

  $\begin{array}{c}X\min =-10\\ X\max =10\\ Y\min =-400\\ Y\max =20\end{array}$

For better view of graph.

Step 8: Press $\boxed{\text{GRAPH}}$ key.

The result obtained on the screen is provided below,

  

Interpretation:

The equation of the function $y=-100x^2$ represents a parabola.

The parabola opens upward.

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

Substitute $y=0$ in the equation $y=-100x^2$ ,

  $\begin{array}{c}0=-100x^2\\ x^2=-\frac{0}{100}\\ x^2=0\\ x=0\end{array}$

Therefore, x- intercept is 0.

The y- intercepts are the points on x -axis where the graph of the equation intersects the y -axis.

Substitute $x=0$ in the equation $y=-100x^2$ ,

  $\begin{array}{c}y=-100x^2\\ y=-100{\left(0\right)}^2\\ y=-100\cdot 0\\ y=0\end{array}$

Therefore, y- intercept are is 0.

Therefore, the equation $y=-100x^2$ is not symmetric about the x -axis.

Recall that the function is symmetric with respect to the y -axis, when x is replaced by -x .

Replace x by $-x$ in the equation $y=-100x^2$ ,

  $\begin{array}{c}y=-100{\left(-x\right)}^2\\ y=-100x^2\\ y=-100x^2\end{array}$

Therefore, the equation $y=-100x^2$ is symmetric about the $y-$ axis Initially the graph of the function $y=-100x^2$ increases when increase the value of $x$ ,the graph is a parabola shaped graph.

Therefore, the function is open downward with axis as y -axis.