The given worksheet asks to complete the table and graph the points based on the function $f(x) = -x^2 + 3x$.

Let's break this down:

Function:

$f(x) = -x^2 + 3x$

Table values:

You are given $x = -1, 0, 1.5, 3, 4$, and you need to find the corresponding $y$ values using the function.

We’ll calculate each:

1. For $x = -1$: $f(-1) = -(-1)^2 + 3(-1) = -1 - 3 = -4$

2. For $x = 0$: $f(0) = -(0)^2 + 3(0) = 0$

3. For $x = 1.5$: $f(1.5) = -(1.5)^2 + 3(1.5) = -2.25 + 4.5 = 2.25$

4. For $x = 3$: $f(3) = -(3)^2 + 3(3) = -9 + 9 = 0$

5. For $x = 4$: $f(4) = -(4)^2 + 3(4) = -16 + 12 = -4$

Completed table:

Graph:

You can now plot the points:

• (-1, -4)
• (0, 0)
• (1.5, 2.25)
• (3, 0)
• (4, -4)

This gives a parabolic curve that opens downward, as expected for a quadratic function with a negative leading coefficient.

Let me know if you need more details or help with graphing!

Related Questions:

1. What is the axis of symmetry of the function $f(x) = -x^2 + 3x$?
2. How would the graph change if the coefficient of $x^2$ were positive?
3. What are the maximum or minimum values of the function $f(x)$?
4. How would the function $f(x)$ behave for very large positive and negative values of $x$?
5. Can you find the x-intercepts of the function?

Tip:

Always check if the function is factorable when looking for key points like intercepts.