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).

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).
Transcript text: Question 6 Examine the table, which contains some points of a quadratic function. \begin{tabular}{|l|l|} \hline$x$ & $f(x)$ \\ \hline-3 & 4 \\ \hline-2 & 0 \\ \hline-1 & -2 \\ \hline 0 & -2 \\ \hline 1 & 0 \\ \hline \end{tabular} 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 $(1,0)$. - Previous
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Solution

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Solution Steps

Step 1: Identify the x x -intercepts

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

  • At x=2 x = -2 , f(x)=0 f(x) = 0 , so (2,0)(-2, 0) is an x x -intercept.
  • At x=1 x = 1 , f(x)=0 f(x) = 0 , so (1,0)(1, 0) is an x x -intercept.
Step 2: Identify the y y -intercept

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

  • At x=0 x = 0 , f(x)=2 f(x) = -2 , so (0,2)(0, -2) is the y y -intercept.
Step 3: Evaluate the given statements
  1. The function has an x x -intercept of (0,2)(0, -2): False (This is the y y -intercept).
  2. The function has an x x -intercept of (2,0)(-2, 0): True.
  3. The function has a y y -intercept of (0,2)(0, -2): True.
  4. The function has an x x -intercept of (1,0)(1, 0): True.
  5. The function has a y y -intercept of (1,0)(1, 0): False (This is an x x -intercept).

Final Answer

The true statements are:

  • The function has an x x -intercept of (2,0)(-2, 0).
  • The function has a y y -intercept of (0,2)(0, -2).
  • The function has an x x -intercept of (1,0)(1, 0).

Thus, the final answer is: True statements: (2,0),(0,2),(1,0)\boxed{\text{True statements: } (-2, 0), (0, -2), (1, 0)}

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