Question

the illustration below shows the graph of ( y ) as a function of ( x ).
complete the following sentences based on the graph of the function.
(enter the ( x )-intercepts from least to greatest.)

• this is the graph of a (\boldsymbol{downarrow}) function.
• the ( y )-intercept of the graph is the function value ( y = \boldsymbol{square} ).
• the ( x )-intercepts of the graph (in order from least to greatest) are located at ( x = \boldsymbol{square} ) and ( x = \boldsymbol{square} ).
• the greatest value of ( y ) is ( y = \boldsymbol{square} ), and it occurs when ( x = \boldsymbol{square} ).
• for ( x ) between ( x = 0 ) and ( x = 6 ), the function value ( y \boldsymbol{downarrow} 0 ).

Explanation:

Step1: Identify function type

The graph is a downward-opening parabola, which is a quadratic function.

Step2: Find y-intercept

The y-intercept is where $x=0$. From the graph, at $x=0$, $y=1$.

Step3: Find x-intercepts

x-intercepts are where $y=0$. From the graph, these are at $x=0$ and $x=6$ (ordered least to greatest).

Step4: Find maximum y-value

The vertex (highest point) of the parabola has $y=9$, occurring at $x=3$.

Step5: Analyze y between x=0 and 6

For $0 < x < 6$, the graph is above the x-axis, so $y > 0$.

Answer:

• This is the graph of a quadratic function.
• The y-intercept of the graph is the function value $y = 1$.
• The x-intercepts of the graph (in order from least to greatest) are located at $x = 0$ and $x = 6$.
• The greatest value of $y$ is $y = 9$, and it occurs when $x = 3$.
• For $x$ between $x = 0$ and $x = 6$, the function value $y > 0$.