Chapter 1.1, Problem 2GP

Solution

To graph: The function and compare that with the standard equation.

Given information:

Graph the function $y=-x^2-5$ and compare it with the graph of $y=x^2$ .

Graph:

The data points to graph the function $y=-x^2-5$ are shown in Table -1. The graphs of the functions $y=-x^2-5$ and $y=x^2$ are shown in Fig. (1).

  

Step 1: Make a table for values of $y=-x^2-5$ , here Table-1.

Step 2: Plot the points shown in Table-1.

Step 3: Draw smooth curve passing through the table points.

Step 4: Compare the graphs of $y=-x^2-5$ and $y=x^2$ shown in Fig. (1).

(a) The graph of the function $y=-x^2-5$ opens down, while that of function $y=x^2$ opens up.

(b) Both graphs have same axis of symmetry y -axis or line $x=0$ .

(c) Graph of function $y=-x^2-5$ has vertex at point $\left(0,-5\right)$ and the graph of function $y=x^2$ at point $\left(0,0\right)$ .

(d) Then distance between the vertices of graph of $y=-x^2-5$ and graph of $y=x^2$ is 5 units.

Interpretation:

The graphs of the quadratic functions are parabolas with axis symmetry $x=0$ and vertex the point $(0,0)$ .