Quadratics

Completing the Square

100

Find the value for c to make the equation a perfect square trinomial. 

x^2+10x+c

c = 5

200

Find the value for c to make the expression a perfect square trinomial. 

x^2 - 70x + c

c = 1225

300

Solve for x using completing the square. 

x^2 + 8x - 9 = 0

x = -9, 1

400

Solve for x using complete the square. 

x^2 + 8x +15 = 0.

x = -5, -3 

500

Solve for x to the nearest tenth using complete the square. 

0.4x^2 + 0.8x = 0.2

x = -2.2, 0.2

Quadratic Formula

100

What is the discriminant of 

x^2-17x-60

529

200

The quadratic equation of

x^2-5x+3=0 has how many roots?

Two roots 

300

Solve for x using the quadratic forumla

x^2 - 7x + 12 = 0

x = 4,3

400

Solve for X using the Quadratic Formula

6x^2-17x+12=0

x=4/3,3/2

500

Solve for x. Round to the nearest tenth. 

x^2 + 20x + 3 = 0

x = -10 ± sqrt(97)

Solve by Factoring/Grouping

100

Simplifly using GCF and difference of squares. 

72x - 242

(6x + 11)(6x - 11)

200

What are the solutions of x?

(x-3)(x+5) = 0

x = 3, -5

300

Factor the quadratic, and solve for x

x^2 - 6x + 5 = 0

x = 5, 1

400

Factor

2x^3 + x^2 + 6x + 3

(x^2 + 3)(2x + 1)

500

solve for x using factoring

8x^2 + 2x - 3 = 0

x = 1/2, -3/4

Transformations

100

Which form should the quadratic be in for the transformations to be easily spotted? 

Vertex form

200

If "h" is negative which side does the graph get translated to?

"h" units to the right

300

What two things does "a" determine in vertex form?

It determines if there is vertical strech or compression, and if the graph is reflected upon the x-axis. 

400

List the transformations of the quadratic function

3(x-1)^(2) + 2

Compression of 3

Right 1

Up 2

500

List all of the transformations that are possible for a quadratic function.  

Graph can be flipped over the x-axis, or can remain normal. 

Graph can be vertically streched, compressed, or can remain normal. 

Graph can go up or down units, or remain normal. 

Graph can go left or right units, or remain normal. 

Graphing

100

Which form should the function be in if you are graphing?

Standard form

200

How many points are needed to create a proper graph?

5

300

What is the first thing you should do when graphing a quadratic? How do you do that?

Finding the Axis of Symetry. -b/2a

400

Tell the definitions of the words. 

Vertex, Axis of Symetry, Zeros, Y - Intercept

Vertex - The highest or lowest point of the graph, depending if it is a min or max graph. The mid point.

Asix of Symetry - The symetrical line in the middle of the parabola. 

Zeros - Roots, or x-intercepts

Y - Intercept - Where the graph crosses the y-axis. 

500

Graph

y = 2x^2 + 8x - 10

Graph should have vertex at (-2, -18), y-int at (0,-10), and check the last point on Desmos.