Answered

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In the [tex]\( xy \)[/tex]-plane, what is the [tex]\( y \)[/tex]-intercept of the graph of the equation [tex]\( y = 6\left(x - \frac{1}{2}\right)(x + 3) \)[/tex]?

A. [tex]\(-9\)[/tex]

B. [tex]\(-\frac{1}{2}\)[/tex]

C. 3

D. 9

Sagot :

GinnyAnswer
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].
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