STANDARDS 14, 19, 20 & 23:
SOLVING QUADRATIC EQUATIONS
Vocabulary
Quadratic Equation: A equation with an x-squared value as it's highest exponent.
Solution: (Also known as a root, x-intercept or zero) is the x-value when the y=0 or visually, it is where the graph hits the x-axis. A quadratic can have one, two or no solutions
Parabola: the u=shape of a quadratic graph
There are 3 ways to solve a quadratic equation: Factoring, Completing the Square or the Quadratic Formula
Solution: (Also known as a root, x-intercept or zero) is the x-value when the y=0 or visually, it is where the graph hits the x-axis. A quadratic can have one, two or no solutions
Parabola: the u=shape of a quadratic graph
There are 3 ways to solve a quadratic equation: Factoring, Completing the Square or the Quadratic Formula
How to Solve by Factoring
How to solve by factoring:
1. Factor the quadratic completely
2. Set each of the factors equal to zero
3. Solve
4. You can check your solutions by substituting them into the original equation, and you should get out '0'
See this example: http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/solve-by-factoring.php
1. Factor the quadratic completely
2. Set each of the factors equal to zero
3. Solve
4. You can check your solutions by substituting them into the original equation, and you should get out '0'
See this example: http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/solve-by-factoring.php
Solve by Completing the Square
How to:
1. Divide all terms by a if a does not equal one
2. Move the c value to the right side
3. Add (b/2)squared to both sides
4. Factor the left hand side (should be a perfect square)
5. Take the square root of both sides.
6. Solve (you should get two solutions)
Watch the video: http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/completing-the-square-solution-example.php
1. Divide all terms by a if a does not equal one
2. Move the c value to the right side
3. Add (b/2)squared to both sides
4. Factor the left hand side (should be a perfect square)
5. Take the square root of both sides.
6. Solve (you should get two solutions)
Watch the video: http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/completing-the-square-solution-example.php
Solve with the Quadratic Formula
How to:
1. Put the equation in standard form
2. Identify a, b, c
3. Solve (there should be two solutions)
Watch this video: http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/quadratic-formula-definition.php
1. Put the equation in standard form
2. Identify a, b, c
3. Solve (there should be two solutions)
Watch this video: http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/quadratic-formula-definition.php
Need help remembering the formula?
here's the song to help you!http://www.schooltube.com/video/adabcffde14c17b9c412/Quadratic%20Formula%20Song%20Rockford%20Christian
The Discriminant
The part under the square root is called the "discriminant" (b-squared minus 4ac)
It helps us determine how many solutions there will be (zero one or two!)
Watch the video to see!
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/quadratic-formula-no-real-solution-test.php
It helps us determine how many solutions there will be (zero one or two!)
Watch the video to see!
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/quadratic-formula-no-real-solution-test.php
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