To find the [tex]\( y \)[/tex]-intercept of the given 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 set to zero.
1. Start with the equation:
[tex]\[ y = 6 \left( x - \frac{1}{2} \right) (x + 3) \][/tex]
2. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = 6 \left( 0 - \frac{1}{2} \right) (0 + 3) \][/tex]
3. Simplify inside the parentheses:
[tex]\[ y = 6 \left( -\frac{1}{2} \right) (3) \][/tex]
4. Multiply the terms:
[tex]\[ y = 6 \times -\frac{1}{2} \times 3 \][/tex]
[tex]\[ y = 6 \times -\frac{3}{2} \][/tex]
[tex]\[ y = -9 \][/tex]
Thus, 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].
