Using the equation f(×)=3(×-1)^2 -4 determine 2f(3) - 7

To solve the expression \(2f(3) - 7\) using the given function \(f(x) = 3(x - 1)^2 - 4\), we need to follow these steps:

### Step 1: Find \(f(3)\)
Substitute \(x = 3\) into the function:

\[
f(3) = 3(3 - 1)^2 - 4
\]

Calculate inside the parentheses first:

\[
f(3) = 3(2)^2 - 4
\]

Now square 2:

\[
f(3) = 3 \cdot 4 - 4
\]

Multiply by 3:

\[
f(3) = 12 - 4
\]

Simplify:

\[
f(3) = 8
\]

### Step 2: Compute \(2f(3) - 7\)

Now that we have \(f(3) = 8\), we can compute \(2f(3) - 7\):

\[
2f(3) - 7 = 2 \cdot 8 - 7
\]

Multiply:

\[
2f(3) - 7 = 16 - 7
\]

Subtract:

\[
2f(3) - 7 = 9
\]

### Final Answer:
\[
2f(3) - 7 = 9
\]

Would you like to know more details or have any questions?

Here are 5 related questions that expand on this topic:

1. How do we determine the vertex of the quadratic function \(f(x) = 3(x - 1)^2 - 4\)?
2. What is the range of the function \(f(x) = 3(x - 1)^2 - 4\)?
3. How do we find the roots of the function \(f(x) = 3(x - 1)^2 - 4\)?
4. How does changing the coefficient 3 in \(f(x) = 3(x - 1)^2 - 4\) affect the graph of the function?
5. Can we express \(f(x) = 3(x - 1)^2 - 4\) in standard form?

**Tip:** When evaluating functions, always start by substituting the given value into the expression step by step to avoid mistakes.

Using the equation f(x)=3(x-1)^2 -4 determine 2f(3) - 7

Learn how to solve the expression 2f(3) - 7 for the quadratic function f(x) = 3(x - 1)^2 - 4. This problem covers key algebraic concepts, including function evaluation and quadratic functions. Suitable for students in Grades 9-10.

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