Quadratic Processes Flashcards
To find x-intercepts for a parabola, the easiest form to use is…
Factored Form
To find y-intercepts for a parabola, the easiest form to use is…
Standard Form
To find x-intercepts for a parabola from Vertex Form there are 3 techniques…
Solve for x after setting y=0; OR
Convert to Factored Form; OR
Use the Quadratic Formula after converting to Standard Form
To find x-intercepts for a parabola in Standard Form there are 2 techniques…
Convert to Factored Form; OR
Use the Quadratic Formula
Even though there are multiple paths to finding x-intercepts, in the end they are all the same as Solving for x after…
Solving for x after setting y=0
Finding y-intercepts, requires Solving for y after…
Solving for y after setting x=0
If a parabola has no x-intercepts, the best way to demonstrate this is…
By showing that the Quadratic Formula is not possible due to it resulting in a negative number under the root sign
which is when b² - 4ac < 0
If a quadratic function can’t be factored using the simple or integer techniques learned in class, there are 2 possibilities…
The Quadratic Formula is required; or the quadratic is not factorable
If it seems a quadratic can’t be converted to factored form to find the x-intercepts, there are 2 possibilities…
The Quadratic Formula is required to find the x-intercepts; or the Quadratic Formula shows that there are no x-intercepts.
It is not possible to convert to Factored Form, if…
b² - 4ac < 0
which is the same as saying…
whenever the Quadratic Formula fails due to a negative value under its root sign
To convert to Vertex Form there are 2 possibilities…
If you know the vertex and 1 other point, use y=a(x-h)² +k directly; OR
If the quadratic is in Standard Form, complete the square
When converting to Factored Form, which 4 factoring techniques could be required?
- Common Factoring
- Simple trinomial factoring, x²+bx+c
- Complex trinomial factoring, ax²+bx+c
- Special Binomial / Difference of Squares, x²-c²
When Completing the Square, what is the side calculation needed to start the process from Standard Form?
Given x²+bx+c, the first step is to calculate (b/2)²
When Completing the Square given x²+6x+2, you have calcuated (6/2)² = 9. Where does this value go in the next step?
x²+6x+2
=(x²+6x+9-9)+2
=(x²+6x+9)-9+2
After converting Standard Form to Vector or Factored Form, what could you do to check your solution?
Expand your solution from Vector or Factored Form back to Standard Form!
