Let's solve this step by step:

Part ⓐ: Evaluate $f(5)$

The function is given as: $f(x) = x^2 - 3x$

To find $f(5)$, substitute $x = 5$ into the function: $f(5) = 5^2 - 3(5) = 25 - 15 = 10$

So, $f(5) = 10$.

Part ⓑ: Solve $f(x) = 4$

The equation is $f(x) = x^2 - 3x = 4$.

We need to solve for $x$. Start by setting up the equation: $x^2 - 3x = 4$

Rearrange it into a standard quadratic form: $x^2 - 3x - 4 = 0$

Now, factor the quadratic equation: $(x - 4)(x + 1) = 0$

Set each factor equal to 0 and solve for $x$: $x - 4 = 0 \quad \Rightarrow \quad x = 4$ $x + 1 = 0 \quad \Rightarrow \quad x = -1$

Thus, the solutions are $x = 4$ and $x = -1$.

Summary:

• $f(5) = 10$
• The solutions to $f(x) = 4$ are $x = 4$ and $x = -1$.

Do you want more details or have any questions?

Here are 5 related questions for practice:

1. Evaluate $f(-2)$ for $f(x) = x^2 - 3x$.
2. Solve $f(x) = 0$ for the same function.
3. What is the vertex of the quadratic function $f(x) = x^2 - 3x$?
4. Solve $f(x) = -2$ for $f(x) = x^2 - 3x$.
5. How would the graph of $f(x) = x^2 - 3x$ look?

Tip: When solving quadratics, try factoring first, but if that doesn't work, use the quadratic formula!