Question

f(x) = 5x2 + 2x − 3What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.

Answer 1

Step-by-step explanation:

Given;

We are given a quadratic function as shown below;

`f(x)=5x^2+2x-3`

Required;

We are required to show the steps required to graph this function.

Step-by-step solution;

To do this, we would need to set up a table of values for x and y.

We shall take input values that is x, and use this to get corresponding output value, that is y.

`\begin{gathered} When\text{ }x=0: \\ y=5(0)^2+2(0)-3 \end{gathered}`
`y=0+0-3=-3`

Therefore, we have the coordinates (0, -3)

`\begin{gathered} When\text{ }x=1: \\ y=5(1)^2+2(1)-3 \end{gathered}`
`y=5+2-3=4`

This gives us the coordinates, (1, 4)

`\begin{gathered} When\text{ }x=2: \\ y=5(2)^2+2(2)-3 \end{gathered}`
`y=20+4-3=18`

This too gives us the coordinates, (2, 18).

Note that the same can be done for the left side of the graph (where the x values are negative).

Hence, using the same procedure as shown above, we would have;

`\begin{gathered} When\text{ }x=-1,y=0 \\ That\text{ }is,\text{ }(-1,0) \end{gathered}`
`\begin{gathered} When\text{ }x=-2,y=13 \\ That\text{ }is,\text{ }(-2,13) \end{gathered}`
`\begin{gathered} When\text{ }x=-3,y=36 \\ That\text{ }is,\text{ }(-3,36) \end{gathered}`

We can go on and plot as many points as the graph page can accommodate using this same procedure.

Next step is to connect the points as shown by the coordinates.

Using a graphing calculator, the graph of the quadratic function given will be as shown below;