The quadratic function  g(x) = 3x^{2} + 6x + 3  has y-intercept. What is the y-intercept of  g(x)?
Question 13Answer

a.
(3, 0)

b.
(0, -3)

c.
(0, 3)

d.
(-3, 0)

To find the y-intercept of a function, we substitute \( x = 0 \) into the function \( g(x) \) and solve for \( g(0) \).

Given:
\[
g(x) = 3x^2 + 6x + 3
\]

Substitute \( x = 0 \):
\[
g(0) = 3(0)^2 + 6(0) + 3 = 3
\]

So, the y-intercept of \( g(x) \) is:
\[
(0, 3)
\]

The correct answer is:
**c. (0, 3)**

Would you like further explanation or details on this process?

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Here are some related questions:

1. How do you find the x-intercepts of a quadratic function?
2. What is the vertex of the function \( g(x) = 3x^2 + 6x + 3 \)?
3. How does the value of \( a \) in \( ax^2 + bx + c \) affect the shape of a quadratic graph?
4. How do you determine if a quadratic function opens upward or downward?
5. Can the y-intercept be used to determine the axis of symmetry?

**Tip:** The y-intercept of any function \( f(x) \) is simply \( f(0) \).

The quadratic function g(x) = 3x^{2} + 6x + 3 has y-intercept. What is the y-intercept of g(x)?

Discover how to find the y-intercept of the quadratic function g(x) = 3x² + 6x + 3. This problem highlights the calculation steps, leading to the conclusion that the y-intercept is (0, 3). Ideal for students in Grades 7-9.

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