Question

Graph the following on the one coordinate system. a. y=-2x^2 b. y=-2(x-3)^2 c. y=-2(x+3)^2

Answer 1

Given: The equations below

`\begin{gathered} a) \\ y=-2x^2 \\ b) \\ -2(x-3)^2 \\ c) \\ y=-2(x+3)^2 \end{gathered}`

To Determine: The graph of the given equations on one coordinate

Solution

Let us get the different points to plot

`\begin{gathered} a)y=-2x^2 \\ x=-2 \\ y=-2(-2)^2=-2(4)=-8 \\ x=-1 \\ y=-2(-1)^2=-2(1)=-2 \\ x=0 \\ y=-2(0)^2=-2(0)=0 \\ x=1 \\ y=-2(1)^2=-2(1)=-2 \\ x=2 \\ y=-2(2)^2=-2(4)=-8 \end{gathered}`

The table of value is as shown below

The table of values for equation in (b) is as shown below

The table of values for the equation in (c) is as shown below

Let us graph each of the given equations using the tables of values as shown below

The graph is as shown above, it can be observed that graph of b is graph of a shifted to the right by 3 units and graph of c is graph of a shifted to the left by 3 units