Question 1
LEVEL 4
Use the table below to plot the equation y=2x^2-2x-4 between -2 and 3.
Select the correct plot from the list below:
A:
B:
C:
D:
CORRECT ANSWER: C
WORKED SOLUTION:
To fill in our table, we need to substitute the x values on the top row into our equation. This will give us the corresponding y values.
\text{When }x=-2 \hspace{1cm}\rightarrow \hspace{1cm}y=2(-2)^2-2(-2)-4=8
\text{When }x=-1 \hspace{1cm}\rightarrow \hspace{1cm}y=2(-1)^2-2(-1)-4=0
\text{When }x=0 \hspace{1cm}\rightarrow \hspace{1cm}y=2(0)^2-2(0)-4=4
\text{When }x=1 \hspace{1cm}\rightarrow \hspace{1cm}y=2(1)^2-2(1)-4=-4
\text{When }x=2 \hspace{1cm}\rightarrow \hspace{1cm}y=2(2)^2-2(2)-4=0
\text{When }x=3 \hspace{1cm}\rightarrow \hspace{1cm}y=2(3)^2-2(3)-4=8
Now that we have completed the table, we can use the x and y values to plot our coordinates.
And finally, we just need to connect the points.
Question 2
LEVEL 4
Use the table below to plot the equation y=x^3-5x^2+7x-3 between 0 and 4.
Select the correct plot from the list below:
A:
B:
C:
D:
CORRECT ANSWER: A
WORKED SOLUTION:
To fill in our table, we need to substitute the x values on the top row into our equation.
This will give us the corresponding y values.
\text{When }x=0 \hspace{1cm}\rightarrow \hspace{1cm}y= (0)^3-5(0)^2+7(0)-3=-3
\text{When }x=1 \hspace{1cm}\rightarrow \hspace{1cm}y= (1)^3-5(1)^2+7(1)-3=0
\text{When }x=2 \hspace{1cm}\rightarrow \hspace{1cm}y= (2)^3-5(2)^2+7(2)-3= -1
\text{When }x=3 \hspace{1cm}\rightarrow \hspace{1cm}y= (3)^3-5(3)^2+7(3)-3=0
\text{When }x=4 \hspace{1cm}\rightarrow \hspace{1cm}y= (4)^3-5(4)^2+7(4)-3=9
Now that we have completed the table, we can use the x and y values to plot our coordinates:
And finally, we just need to connect them.
Question 3
LEVEL 4
Choose the correct plot for the equation y=x^2+2x+2
Select the correct plot from the list below:
A: 
B: 
C: 
D: 
CORRECT ANSWER: A
WORKED SOLUTION:
We need to substitute various x values into our equation to find the corresponding y values.
\text{When }x=-4 \hspace{1cm}\rightarrow \hspace{1cm}y=(-4)^2+2(-4)+2=10
\text{When }x=-2 \hspace{1cm}\rightarrow \hspace{1cm}y=(-2)^2+2(-2)+2=2
\text{When }x=0 \hspace{1cm}\rightarrow \hspace{1cm}y=(0)^2+2(0)+2=2
\text{When }x=2 \hspace{1cm}\rightarrow \hspace{1cm}y=(2)^2+2(2)+2=10
We can now use the x and y values to plot the graph:
Question 4
LEVEL 4
Choose the correct plot for the equation y=-x^2+3
Select the correct plot from the list below:
A: 
B: 
C: 
D: 
CORRECT ANSWER: A
WORKED SOLUTION:
We need to substitute various x values into our equation to find the corresponding y values.
\text{When }x=-3 \hspace{1cm}\rightarrow \hspace{1cm}y=-(-3)^2+3 = -6
\text{When }x=-1 \hspace{1cm}\rightarrow \hspace{1cm}y=-(-1)^2+3 = 2
\text{When }x=0 \hspace{1cm}\rightarrow \hspace{1cm}y=-(0)^2+3 = 3
\text{When }x=1 \hspace{1cm}\rightarrow \hspace{1cm}y=-(1)^2+3 = 2
\text{When }x=3 \hspace{1cm}\rightarrow \hspace{1cm}y=-(3)^2+3 = -6
We can now use the x and y values to plot the graph:
Question 5
LEVEL 4
A graph has the following equation: y = -3x^3 + 2x^2 - 97
Without any calculation, what type of graph is it?
Select the correct statement from the list below.
A: It is a cubic graph
B: It is a quadratic graph
C: It is neither a cubic graph nor a quadratic graph
D: I would need plot the graph to be able to tell
CORRECT ANSWER: A
WORKED SOLUTION:
Any quadratic graph has the form y = ax^3 + bx^2 + cx + d