Find the Roots/Zeroes
Types of Solutions by Graphing
Determining Types of Roots by the Discriminant
Find the X-Intercepts
Misc.
100
Name at least three ways you could find the roots/zeroes/x-intercepts of a quadratic equation.
Factoring Graphing Quadratic Equation Completing the Square Using a Table of Values
100
The parabola goes through the x-axis twice. How many solutions are there and are they real or imaginary?
What is 2, real
100
The discriminant is -31. How many roots will it have and what type? (rational, irrational, imaginary)
What is 2 imaginary roots
100
x^2 + 12x + 20 = 0
What is -10 and -2?
100
What number does the discriminant need to be to have just one solution?
What is 0?
200
x^2 + 8x + 12 = 0
What is -6 and -2?
200
The parabola goes through the x-axis once. How many solutions are there and are they real or imaginary?
What is one, real
200
Take the discriminant of x^2 - 12x = 28. How many roots will it have and what type? (rational, irrational, imaginary)
What is two, rational roots
200
x^2 - 9x + 18 = 0
What is 6 and 3?
200
Can you ever have "0" solutions?
No, you will always have at least one.
300
9x^2 - 6x - 4 = 0
What is 1/3
300
The parabola goes through the x-axis zero times. How many solutions are there and are they real or imaginary?
What is 2, imaginary
300
Take the discriminant of x^2 + 22x +121 = 0. How many roots will it have and what type? (rational, irrational, imaginary)
What is one, rational
300
x^2 - 6x + 2 = 0
What is 3 + sqrt(7) and 3 - sqrt(7)
300
Complete the square: x^2 + 8x + ____ = 3 + ______
What is 16?
400
x^2 + 3x -3 = 0
What is -3 + sqrt(21)/2 and -3 - sqrt(21)/2
400
The parabola goes through the x-axis twice. How many solutions are there and are they real or imaginary?
What is 1, real
400
Take the discriminant of 2x^2 + 4x - 5 = 0. How many roots will it have and what type? (rational, irrational, imaginary)
What is two, irrational roots.
400
x^2 + 13 = 6x
What is 3 + 2i and 3 - 2i
400
Write in vertex form: y = -x^2 - 4x + 18
What is y = -(x + 2)^2 + 22
500
x^2 - 2x + 5 = 0
What is 1 + 2i and 1 - 2i
500
The parabola goes through the y-axis once. How many solutions are there and are they real or imaginary?
What is cannot be determined by the information given
500
Take the discriminant of x^2 - 4x = -13. How many roots will it have and what type? (rational, irrational, imaginary)
What is two, complex roots?
500
3x + 6 = -6x^2
What is -1 + (i sqrt(15))/4 and -1 - (i sqrt(15))/4
500
Name the vertex, axis of symmetry, and direction of opening for the following equation: y = -3 (x - 4)^2 + 6
Vertex: (4, 6) Axis of Symmetry: x = 4 Direction of Opening: Downward
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