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!
To find the Vertex, there are 3 possibilities…
Convert to Vertex Form; OR
From Factored Form average the x-intercepts to find the axis of symmetry; OR
From the Quadratic Formula average the x-intercepts to find the axis of symmetry
The axis of symmetry has 1 extra step to find the y-value of the vertex
