Contents
Go directly to a video or scroll through them down below. [Some of this contents is out of whack, and I'm still working on some of the vids for this section. I hope to have them up by the end of the first week in April - sorry for any inconvenience – Jeff.]
- What it means to factor a quadratic equation of the form x2 + Bx + C = 0
- Transforming between the vertex form, f(x) = A(x - h)2 + k, and standard form, f(x) = Ax2 + Bx + C, of a quadratic equation; finding the vertex.
- Transforming between the vertex form and the standard form: an example.
- Completing the square: Example 1
- Completing the square: Example 2
- Completing the square: Yet another example
- Derivation of the quadratic formula (don't miss this one)
- Completing the square to obtaincomplex roots
- The vertex form of a quadratic function
- Graphing (1 of 3) a quadratic function with real integer roots
- Graphing (2 of 3) a quadratic function with non-integer real roots
- Graphing (3 of 3) a quadratic function with imaginary roots
1. What it means to factor a quadratic equation of the form
x2 + Bx + C = 0 (A = 1)
Minutes of your life: 2:42
2. Relationship between vertex and standard form of a quadratic function: A(x - h)2 + k ↔ Ax2 + Bx + C
Minutes of your life: 2:21
3. Example of transforming between the vertex and standard forms of a quadratic function: A(x - h)2 + k ↔ Ax2 + Bx + C
Minutes of your life: 2:50
4. Completing the square: Example 1
In this example we complete the square to find the roots of a function for which we already know the roots. It's a good example to work through to see that completing the square works!
Minutes of your life: 2:46
5. Completing the square: Example 2
In this example, the quadratic function f(x) = 8x2 - 20x - 3 has real roots, but it's not factorable. We complete the square to find the exact roots of the function. There is no difference between completing the square and using the quadratic formula, but I think that knowing how to complete the square will help you to understand a lot about basic algebra steps. You should learn it!
Minutes of your life: 2:58
7. Derivation of the quadratic formula – a must-see.
In this example, we start with f(x) = Ax2 + Bx + C and complete the square to derive the quadratic formula.
Minutes of your life: 2:04 (and well worth it!)
8. Completing the square to obtain imaginary roots
In this example, we find the roots of f(x) = 3x2 - 4x + 7, which are imaginary (or more accurately, are complex with non-zero imaginary parts. We also use the discriminant to show how to determine before-hand that the roots of a quadratic function will be non-real.
Minutes of your life: 2:51
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