Find the absolute value of the complex number:
3-4i
What is 5
100
Use the quadratic formula to solve the quadratic equation:
6x^2 + 9x = -3
On your whiteboard, I must see all numbers plugged into the quadratic equation, and a final answer to earn points.
What is x=[-9±√(81-4(6)(3))]/[2*6]
Simplified: x=-1 or -1/2
100
Graph (using vertex form):
y=(x-2)^2 - 2
What is (I will check your graph).
Vertex: (2,-2)
Possible 2 points: (0,2) and (4,2)
100
Graph:
y ≤ -x^2 + 4x + 2
What is (I will check your answer)
Solid Line
Vertex: (2,6)
Possible 2 points: (0,2) and (4,2)
Inside of parabola is shaded
100
Find the discriminant and determine the number of real solutions:
2x^2+x=5
What is 41; 2 real solutions
200
Write the complex equation in standard form:
(4+3i) - (-2+4i)
What is (6-i)
200
Solve the quadratic equation by factoring:
8y^2 - 28y - 60 = 0
You must show the factored equation and the solution(s) to get the points.
What is 4(2y+3)(y-5)=0
y = -3/2, 5
200
Graph the quadratic equation by factoring:
y=-x^2+2x-1
What is y=-(x-1)^2. (I will check your graph)
Vertex: (-1,0)
Possible 2 points: (0,-1) and (-2,-1)
200
Solve the inequality by graphing:
x^2 - 6x + 5 < 0
Notice that there is no y.
What is (I will check your answer)
Dotted line
Vertex: (3,-4)
Possible 2 points: (0,5) and (6,5)
Inside of parabola on number line is shaded
200
Find the discriminant and determine the number of real solutions:
7x^2 - 4x + 1
What is -12 and no real solutions (2 imaginary solutions).
300
Write the complex equation in standard form:
(7-6i)/(4+3i)
What is (2/5)-(9/5)i or (2-9i)/5
300
Solve the equation by completing the square:
3x^2 - 6x + 12 = 0
What is (x-1)^2 + 3=0
x=1+i√3, 1 - i√3
300
Graph the quadratic equation:
y=4 - x^2
[3 points must be identified]
What is (I will check your graph)
Vertex: (0,4)
x-Intercepts: (2,0) and (-2,0)
300
Graph y
What is (I will check your graph)
Dotted line
Vertex: (1,-1)
Possible 2 points: (0,0) and (2,0)
Outside of parabola is shaded
300
Find the discriminant and determine the number of real solutions. Then solve:
x^2 = 8x - 35
What is -76; No real solutions (2 complex solutions); x=4±i√19.
400
Write the complex equation in standard form:
(7-4i)(-1+2i)
What is (1+18i).
400
Solve the quadratic equation using any method:
3x^2 + 4x - 5 = 0
What is x=(-2 ± √19)/3.
400
Graph the quadratic equation:
y = 2(x+4)(x-2)
[3 points must be identified]
What is (I will check your graph).
Vertex: (1, -10)
x-Intercepts: (-4,0) and (2,0)
400
Graph the inequality using any method:
y < 2x^2 + 12x + 15
What is (I will check your graph).
Dotted line
Vertex: (-3,-3)
Possible 2 points: (0,15) and (-6,15)
Outside of parabola is shaded
400
The general formula for vertex form is y=a(x-h)^2+k.
Given the vertex of a quadratic graph is (-2,5); the point (-1,3) is on the graph, solve for a and write the equation in vertex form.
What is a=-2; y=-2(x+2)+5
500
What is the difference between a complex number and imaginary number?
What is complex numbers are in the form a+bi, whereas imaginary numbers are in the form bi.
Note: Imaginary numbers are a subset of the complex numbers (real numbers are also a subset of the complex numbers).
500
Write a quadratic equation in standard form which passes through the following points:
(-2,30), (1,6), (3,40)
What is 5x^2 - 3x + 4
500
The roots (solutions) of a quadratic equation are x=2-3i or x=2+3i. Notice that complex solutions of quadratic equations come in conjugate pairs.
Determine the quadratic equation; graph.
What is x^2 - 4x + 13. I will check your graph.
Vertex: (2,9)
Possible 2 points: (0,13) and (4,13)
500
Graph the system of inequalities:
y≤-x^2 + 9
y≥x^2 + 5x - 6
What is (I will check your answer)
Both Graphs: solid lines; Inner part is shaded
Graph 1:
Vertex: (0,9); 2 points: (±3,0)
Graph 2:
Vertex: (-2.5, -12.25); 2 points: (0,-6) and (-5,-6)
500
Write the complex number in standard form:
(4-3i)/(9+2i)