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