Quadratic Facts
When solving quadratic equations, we are trying to find what feature of the parabola?
x-intercepts
This is the point where a quadratic function crosses the y-axis
y-intercept
Factor with GCF and Solve
4x^2+8x=0
4x(x+2)=0
x=0 and x=-2
Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0
x = 7 x = -2
or x = { 7, -2}
Find the best method for solving the quadratic equation below:
x^2=4
x=2 and x=-2
What are the three different types of solutions we can have when solving quadratics
No solution, One solution or Two solutions
This point is the minimum or maximum point of a parabola (where it turns around).
Vertex
Factor with GCF
3x^2-9x=0
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3x(x-3)=0
x=0 and x=3
Solve the following quadratic equation by factoring. x2+3x+2 = 0
x = -2 x = -1
Solve with square roots:
3x^2=27
x=-3 and x=3
How do we know a quadratic function does not have solutions when looking at a graph?
It does not touch or pass through the x-axis
The __________ form of quadratic equations is useful for finding the x-intercepts.
Factored
Factor with GCF
5x^2-25x=0
5x(x-5)=0
x=0 and x=5
Solve the following quadratic equation by factoring. x2 - 6x + 5 = 0
x = 5 x = 1
Solve with square roots
x^2+4=20
x=-4 and x=4
How do we know a quadratic function does not have a solution? (What type of number can you not take the square root of?)
There will be a negative number under the square root.
Draw a sketch of a parabola and label the following features:
y-intercept, x-intercepts, vertex (maximum)
Answers will vary.
Solve the following quadratic equation by factoring.
x2 - 6x - 27 = 0
x = 9 x = -3
Solve with square roots:
4x^2+2=18
x=2 or x=-2
Solve by factoring:
x2+6x = -9
(x+3)(x+3)=0
x=-3
Solve with square roots:
6x^2-12=138
x=5 and x=-5