To determine the [tex]\(y\)[/tex]-intercept of the equation [tex]\(y = 6\left(x - \frac{1}{2}\right)(x + 3)\)[/tex], we need to find the value of [tex]\(y\)[/tex] when [tex]\(x\)[/tex] is equal to 0.
1. Begin by setting [tex]\(x = 0\)[/tex] in the equation.
[tex]\[
y = 6\left(0 - \frac{1}{2}\right)(0 + 3)
\][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[
y = 6\left(-\frac{1}{2}\right)(3)
\][/tex]
3. Multiply the values:
[tex]\[
y = 6 \cdot \left(-\frac{1}{2}\right) \cdot 3
\][/tex]
4. Perform the multiplication step-by-step:
[tex]\[
6 \cdot \left(-\frac{1}{2}\right) = -3
\][/tex]
[tex]\[
-3 \cdot 3 = -9
\][/tex]
Thus, the [tex]\(y\)[/tex]-intercept of the graph is [tex]\(-9\)[/tex].
Therefore, the correct answer is [tex]\(-9\)[/tex].
