Questions: Question 6 Examine the table, which contains some points of a quadratic function. x f(x) -3 4 -2 0 -1 -2 0 -2 1 0 Which statements are true about the intercepts of the function? Select all that apply. The function has an x-intercept of (0,-2). The function has an x-intercept of (-2,0). The function has a y-intercept of (0,-2). The function has an x-intercept of (1,0). The function has a y-intercept of (1,0).

Solution Steps

An \( x \)-intercept occurs where \( f(x) = 0 \). From the table:

• At \( x = -2 \), \( f(x) = 0 \), so \((-2, 0)\) is an \( x \)-intercept.
• At \( x = 1 \), \( f(x) = 0 \), so \((1, 0)\) is an \( x \)-intercept.

A \( y \)-intercept occurs where \( x = 0 \). From the table:

• At \( x = 0 \), \( f(x) = -2 \), so \((0, -2)\) is the \( y \)-intercept.

1. The function has an \( x \)-intercept of \((0, -2)\): False (This is the \( y \)-intercept).
2. The function has an \( x \)-intercept of \((-2, 0)\): True.
3. The function has a \( y \)-intercept of \((0, -2)\): True.
4. The function has an \( x \)-intercept of \((1, 0)\): True.
5. The function has a \( y \)-intercept of \((1, 0)\): False (This is an \( x \)-intercept).

Final Answer