Show:
Graphs
Discriminant
Solving(Completing the square and quadratic formula)
Transformations
AOS and Vertex
100

What is a solution on a graph?

x-intercepts, roots, zeroes

100
What is the discriminant of x²+8x=-4. 

x²+8x+4=0. 64-16. The discriminant is 48. 

100

x2+6x-7=0


1 or -7

100

how does f(x)-x2 differ from g(x)=x2+1

g(x) is different because it is one unit up on the graph.

100

Find the axis of symmetry for the equation: y=4x2+8x+42

Using the formula -b/2a, we get -8/2(4), which is also equal to -1.

200

Is the vertex of -y=x²-2x a maximum or minimum, and how do you know?

It is a maximum. When u divide by negative 1 to make it a positive 1, you get y=-x²+2x. Since the coefficient of x² is negative, the parabola opens downwards, and therefore, the vertex is a maximum point.  
200
How many real solutions does the quadratic equation x²-4x+4=0 have?

The discriminant is (-4)²-4*4. This is 16-16. The discriminant is 0, which means there is 1 real solution. 

200

If decimal, round to the tenth.

2x2+12x+3=0 Hint:Quadratic Formula


-0.2 and -5.7

200

How does f(x)=x2 relate to g(x)=(x-2)2-1

g(x) relates because it is moved 2 units to the right and 1 unit down.

200

Find the AOS of the equation below:

y=-3x2-300x+65

Using the formula -b/2a, we get 300/2(-3), which is 300/-6. The answer is -50.

300

What is the y intercept of f(x)=x²+2x+7

(0,7)

300

How many solutions does x²+3x+2 have?

The discriminant is 1. Therefore, 2 real solutions. 

300

x2+20x+11=-8 Solve using Completing the Square

The solutions are -1 or -19.

300
How does f(x)=x2 relate to g(x)=2(x-2)2+5

g(x) relates because the line is stretched, two units to the right, and 5 units up.

300

Find the vertex of the following equation: y=5x2-20x+35

The vertex is (2,15). First we find the AOS, which is x=2. We plug this in and we get 15.

400

What is the y intercept of f(x)=2(x-1)²+2?

The y intercept is (0, 4). 
400

How many real solutions does x²-7x-12=0 have?

49+48=97. 2 real solutions because 97>0. 

400

6x2-45=-12x

3 or -15

400

How does f(x)=x2 relate to g(x)=1/3(x-7)2-4

This line, g(x), is compressed, moved 7 units right, and moved 4 units down from f(x).

400

Find the AOS of the following equation: y=2x2+23x-43

The AOS of this equation is x=-23/4. 

500

Graph and solve the quadratic equation 2x²+18x-20=0.

x=1, -10

500

What is the discriminant of the equation 5x+12=-2x².

Move 2x² over. 2x²+5x+12=0. 25-4*2*12. 25-96. -71. The discriminant is -71. 

500

x2-6x+4 (Complete The Square)

 0.8 and 5.2

500

How does f(x)=x2 relate to the line g(x)=-1/4(x+12)2-12

g(x) relates because the line is reflected off the x axis, compressed, moved 12 units to the left, and 12 units down.
500

Find the vertex of the following equation: y=3x2-24x+43

The vertex is (4,-5). First, we use -b/2a to get 24/6, which is 4. Then we plug it in to get 48-96+43, which is -5.