Question

question 18

which of the following describes the end behavior of a graph?

• the lowest point of the graph.
• the highest point of the graph.
• telling where the graph is increasing or decreasing.
• telling what the ends of the graph is doing.

question 19

what is the vertex of (f(x) = (x - 1)^2 - 4)?

• ((1, 4))
• ((4, 1))
• ((1, -4))
• ((-1, -4))

Explanation:

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<reasoning>

Define end behavior of a graph

Using the End Behavior knowledge point
\[
\text{End behavior describes the behavior of } f(x) \text{ as } x \to \infty \text{ and } x \to -\infty.
\]
This corresponds to telling what the ends of the graph are doing.

Identify the vertex of the quadratic function

Using the Vertex of Parabola knowledge point
\[

$$\begin{aligned} &f(x) = a(x-h)^2 + k\\ &f(x) = (x-1)^2 - 4\\ &(h, k) = (1, -4) \end{aligned}$$

\]
</reasoning>

<answer>

Question 18

<mcq-option>The lowest point of the graph.</mcq-option>
<mcq-option>The highest point of the graph.</mcq-option>
<mcq-option>Telling where the graph is increasing or decreasing.</mcq-option>
<mcq-correct>Telling what the ends of the graph is doing.</mcq-correct>

Question 19

<mcq-option>\((1,4)\)</mcq-option>
<mcq-option>\((4,1)\)</mcq-option>
<mcq-correct>\((1,-4)\)</mcq-correct>
<mcq-option>\((-1,-4)\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Define end behavior of a graph

Using the End Behavior knowledge point
\[
\text{End behavior describes the behavior of } f(x) \text{ as } x \to \infty \text{ and } x \to -\infty.
\]
This corresponds to telling what the ends of the graph are doing.

Identify the vertex of the quadratic function

Using the Vertex of Parabola knowledge point
\[

$$\begin{aligned} &f(x) = a(x-h)^2 + k\\ &f(x) = (x-1)^2 - 4\\ &(h, k) = (1, -4) \end{aligned}$$

\]
</reasoning>

<answer>

Question 18

<mcq-option>The lowest point of the graph.</mcq-option>
<mcq-option>The highest point of the graph.</mcq-option>
<mcq-option>Telling where the graph is increasing or decreasing.</mcq-option>
<mcq-correct>Telling what the ends of the graph is doing.</mcq-correct>

Question 19

<mcq-option>\((1,4)\)</mcq-option>
<mcq-option>\((4,1)\)</mcq-option>
<mcq-correct>\((1,-4)\)</mcq-correct>
<mcq-option>\((-1,-4)\)</mcq-option>
</answer>

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