Question

Find the graph of Y equals negative X squared plus 5X -6 by making a table of a few values and plotting the points

Answer 1

Given the function:

`y=-x^2+5x-6`

Let's find the graph of the function by making a table of few values and plotting the points.

Let's find 3 different points by inputting random values for x and solve for y.

• When x = 0:

Substitute 0 for x and solve for y

`\begin{gathered} y=-0^2+5(0)-6 \\ y=0+0-6 \\ y=-6 \\ \\ \text{ Here, we have the point:} \\ (0,\text{ -6\rparen} \end{gathered}`

• When x = 2:

Substitute 2 for x and solve for y

`\begin{gathered} y=-(2)^2+5(2)-6 \\ y=-4+10-6 \\ y=0 \\ \\ Here,\text{ we have the point:} \\ (2,\text{ 0\rparen} \end{gathered}`

• When x = 3:

Substitute 3 for x and solve for y

`\begin{gathered} y=-(3)^2+5(3)-6 \\ y=-9+15-6 \\ y=0 \\ \\ \text{ Here, we have the point:} \\ (3,\text{ 0\rparen} \end{gathered}`

• When x = 1:

`\begin{gathered} y=-(1)^2+5(1)-6 \\ y=-1+5-6 \\ y=-2 \\ \\ We\text{ have the point:} \\ (1,\text{ -2\rparen} \end{gathered}`

Therefore, we have the table of values representing the function:

Now, let's plot the points to find the graph:

(0, -6), (1, -2), (2, 0), (3, 0)

We have the graph below: