Completing the Square
Find the value for c to make the equation a perfect square trinomial.
x^2+10x+c
c = 5
What is the discriminant of
x^2-17x-60
529
Simplifly using GCF and difference of squares.
72x - 242
(6x + 11)(6x - 11)
Which form should the quadratic be in for the transformations to be easily spotted?
Vertex form
Which form should the function be in if you are graphing?
Standard form
Find the value for c to make the expression a perfect square trinomial.
x^2 - 70x + c
c = 1225
The quadratic equation of
x^2-5x+3=0 has how many roots?
Two roots
What are the solutions of x?
(x-3)(x+5) = 0
x = 3, -5
If "h" is negative which side does the graph get translated to?
"h" units to the right
How many points are needed to create a proper graph?
5
Solve for x using completing the square.
x^2 + 8x - 9 = 0
x = -9, 1
Solve for x using the quadratic forumla
x^2 - 7x + 12 = 0
x = 4,3
Factor the quadratic, and solve for x
x^2 - 6x + 5 = 0
x = 5, 1
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.
What is the first thing you should do when graphing a quadratic? How do you do that?
Finding the Axis of Symetry. -b/2a
Solve for x using complete the square.
x^2 + 8x +15 = 0.
x = -5, -3
Solve for X using the Quadratic Formula
6x^2-17x+12=0
x=4/3,3/2
Factor
2x^3 + x^2 + 6x + 3
(x^2 + 3)(2x + 1)
List the transformations of the quadratic function
3(x-1)^(2) + 2
Compression of 3
Right 1
Up 2
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.
Solve for x to the nearest tenth using complete the square.
0.4x^2 + 0.8x = 0.2
x = -2.2, 0.2
Solve for x. Round to the nearest tenth.
x^2 + 20x + 3 = 0
x = -10 ± sqrt(97)
solve for x using factoring
8x^2 + 2x - 3 = 0
x = 1/2, -3/4
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.
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.