To find the [tex]\( y \)[/tex]-intercept of the graph of the equation [tex]\( y = 6\left(x - \frac{1}{2}\right)(x + 3) \)[/tex], we need to determine the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 0. The [tex]\( y \)[/tex]-intercept occurs when [tex]\( x = 0 \)[/tex].
Given the equation:
[tex]\[ y = 6\left(x - \frac{1}{2}\right)(x + 3) \][/tex]
Set [tex]\( x \)[/tex] to 0:
[tex]\[ y = 6\left(0 - \frac{1}{2}\right)(0 + 3) \][/tex]
Simplify inside the parentheses first:
[tex]\[ y = 6\left(-\frac{1}{2}\right)(3) \][/tex]
Multiply the terms inside the parentheses:
[tex]\[ y = 6 \times -\frac{1}{2} \times 3 \][/tex]
Calculate the product:
[tex]\[ y = 6 \times -\frac{3}{2} = 6 \times -1.5 \][/tex]
Finally, multiply:
[tex]\[ y = -9 \][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of the graph of the equation [tex]\( y = 6\left(x - \frac{1}{2}\right)(x + 3) \)[/tex] is [tex]\(-9\)[/tex].
So the correct answer is:
[tex]\[ -9 \][/tex]
