Given the function 𝑓(𝑥)=𝑥2−3𝑥:f(x)=x2−3x:

ⓐ Evaluate 𝑓(5).f(5).

ⓑ Solve 𝑓(𝑥)=4.

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!

Given the function f(x)=x^2−3x: ⓐ Evaluate f(5). ⓑ Solve f(x)=4.

Learn how to evaluate the quadratic function f(x) = x^2 - 3x by finding f(5) and solving f(x) = 4. This step-by-step solution covers key concepts such as function evaluation, factoring, and solving quadratic equations. Ideal for students in Grades 8-10.

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