Question

c) f(x) = 3x² - 3x - 6

Explanation:

Assuming we need to find the x - intercepts of the function \( f(x)=3x^{2}-3x - 6\) (a common task with quadratic functions), here's the step - by - step solution:

Step 1: Set \(f(x) = 0\)

To find the x - intercepts, we set \(y = f(x)=0\). So we have the equation \(3x^{2}-3x - 6=0\).

Step 2: Simplify the equation

We can divide the entire equation by 3 to simplify it. \(\frac{3x^{2}-3x - 6}{3}=\frac{0}{3}\), which gives us \(x^{2}-x - 2 = 0\).

Step 3: Factor the quadratic

We need to factor \(x^{2}-x - 2\). We look for two numbers that multiply to - 2 and add up to - 1. The numbers are - 2 and 1. So, \(x^{2}-x - 2=(x - 2)(x+1)=0\).

Step 4: Solve for x

Using the zero - product property, if \((x - 2)(x + 1)=0\), then either \(x-2 = 0\) or \(x + 1=0\).

• If \(x-2=0\), then \(x = 2\).
• If \(x + 1=0\), then \(x=-1\).

Answer:

The x - intercepts of the function \(f(x)=3x^{2}-3x - 6\) are \(x=-1\) and \(x = 2\). If we were asked for the roots (or x - intercepts) of the function, the solutions are \(x=-1\) and \(x = 2\).