Information
You have already completed the quiz before. Hence you can not start it again.
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
-
Question 1 of 4
Incorrect
Loaded: 0%
Progress: 0%
0:00
The difference of two squares, a2-b2, can be factored as the sum and and difference of a and b (a+b)(a-b)
First, change the inequality sign into an equal sign and find the x values
3x2-3 |
= |
0 |
3(x2-1) |
= |
0 |
Factor out 3 |
3(x+1)(x-1) |
= |
0 |
Difference of two squares |
x+1 |
= |
0 |
x+1 -1 |
= |
0 -1 |
x |
= |
-1 |
x-1 |
= |
0 |
x-1 +1 |
= |
0 +1 |
x |
= |
1 |
Mark these 2 points on the x axis.
Next, substitute x=0 to the function to get the y intercept
y |
= |
3x2-3 |
y |
= |
3(0)2-3 |
Substitute x=0 |
y |
= |
0-3 |
y |
= |
-3 |
Mark this point on the y axis.
Form a parabola by connecting the points
Since we are looking for y<0, the values are below the x axis
-
Question 2 of 4
Incorrect
Loaded: 0%
Progress: 0%
0:00
First, replace the inequality with an equal sign and solve for x using the Quadratic Formula
x |
= |
−b±√b2−4ac2a |
Quadratic Formula |
|
|
= |
−3±√32−4(2)(−7)2(2) |
Plug in the values of a,b and c |
|
|
= |
−3±√9+564 |
|
|
= |
−3±√654 |
Write each root individually
Mark these two points on the x axis
Next, find the y intercept by substituting x=0
y |
= |
2x2+3x-7 |
y |
= |
2(0)2+3(0)-7 |
Substitute x=0 |
y |
= |
0-0-7 |
y |
= |
-7 |
Form a parabola by connecting the points
Since we are looking for y≥0, the values are on or above the x axis
Hence, x≤-2.766 and x≥1.266
-
Question 3 of 4
Graph the inequality:
y>x2-3x-4
Incorrect
Loaded: 0%
Progress: 0%
0:00
Remember the following notations when graphing inequalities.
Symbol |
Solid / Dotted |
< |
Dotted Line |
> |
Dotted Line |
≤ |
Solid Line |
≥ |
Solid Line |
First, equate the function to 0 and solve for x by factoring
y |
> |
x2-3x-4 |
0 |
= |
x2-3x-4 |
x2-3x-4 |
= |
0 |
x-4 |
= |
0 |
x-4 +4 |
= |
0 +4 |
x |
= |
4 |
x+1 |
= |
0 |
x+1 -1 |
= |
0 -1 |
x |
= |
-1 |
Mark these 2 points on the x axis
Next, find the y intercept by substituting x=0
y |
= |
x2-3x-4 |
y |
= |
(0)2-3(0)-4 |
Substitute x=0 |
y |
= |
0-0-4 |
y |
= |
-4 |
Now, connect the points to form a parabola
Remember to use a dotted line because of the > sign
To determine which region to shade, test the origin by substituting (0,0) to the original function
y |
> |
x2-3x-4 |
0 |
> |
(0)2-3(0)-4 |
Substitute values |
0 |
> |
0-0-4 |
0 |
> |
-4 |
This is true, which means the region that includes the origin must be shaded
-
Question 4 of 4
Graph the system of inequalities:
Incorrect
Loaded: 0%
Progress: 0%
0:00
Remember the following notations when graphing inequalities.
Symbol |
Solid / Dotted |
< |
Dotted Line |
> |
Dotted Line |
≤ |
Solid Line |
≥ |
Solid Line |
First, graph the first inequality
Start by equating the function to 0 and solving for x by factoring
x-3 |
= |
0 |
x-3 +3 |
= |
0 +3 |
x |
= |
3 |
x+1 |
= |
0 |
x+1 -1 |
= |
0 -1 |
x |
= |
-1 |
Mark these 2 points on the x axis
Next, find the axis of symmetry
x |
= |
−b2a |
Axis of Symmetry |
|
x |
= |
−(−4)2(1) |
Substitute values |
|
x |
= |
42 |
|
x |
= |
2 |
Substitute x=2 to the equation to find the value of y for the vertex
y |
= |
x2-4x+3 |
y |
= |
22-4(2)+3 |
Substitute x=2 |
y |
= |
4-8+3 |
y |
= |
-1 |
This means that the vertex is at (2,-1)
Find the y intercept by substituting x=0
y |
= |
x2-4x+3 |
y |
= |
02-4(0)+3 |
Substitute x=0 |
y |
= |
0-0+3 |
y |
= |
3 |
Now, connect the points to form a parabola
Remember to use a solid line because of the ≥ sign
To determine which region to shade, test a point by substituting (2,0) to the original function
y |
≥ |
x2-4x+3 |
0 |
≥ |
22-4(2)+3 |
Substitute values |
0 |
≥ |
4-8+3 |
0 |
≥ |
-1 |
This is true, which means the region that covers (2,0) must be shaded
This time, graph the second inequality
Start by equating the function to 0 and solving for x by factoring
2-x |
= |
0 |
2-x +x |
= |
0 +x |
2 |
= |
x |
x |
= |
2 |
2+x |
= |
0 |
2+x -x |
= |
0 -x |
2 |
= |
-x |
x |
= |
-2 |
Mark these 2 points on the x axis
Next, find the axis of symmetry
x |
= |
−b2a |
Axis of Symmetry |
|
x |
= |
−02(−1) |
Substitute values |
|
x |
= |
0 |
The axis of symmetry is at x=0 or the y axis
Substitute x=0 to the equation to find the value of y for the vertex
y |
= |
4-x2 |
y |
= |
4-02 |
Substitute x=0 |
y |
= |
4 |
This means that the vertex is at (0,4)
Since this point lies on the y axis, it is also the y intercept
Now, connect the points to form a parabola
Remember to use a dotted line because of the < sign
To determine which region to shade, test the origin by substituting (0,0) to the original function
y |
< |
4-x2 |
0 |
< |
4-02 |
Substitute values |
0 |
< |
4 |
This is true, which means the region that covers (0,0) must be shaded
Finally, highlight the overlapping region of the two inequalities