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13 terms

Quadratic Functions

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standard form
y=ax^2+bx+c
factored form
y=a(x-p)(x-q)
vertex form
y=a(x-h)^2+v

vertex= (h,v)
How can you solve from vertex form?
Completing the square
How can you solve from factored form?
Factoring
How can you solve from standard form?
Quadratic formula*

*when 0=ax^2+bx+c
discriminant=
b^2-4ac (what's under the root)
How to find the x-coordinate of vertex:
from standard: -b/2a
from factored: (p-q)/2
the discriminant is used in order to find...
how many x-ints there are

+ discriminant=2 x-ints
- discriminant= 0 x-ints
when discriminant=0, there is one x-int, which is also the vertex

*b/c you can't sq root a negative number, and root 0 is 0, but root any positive number will have both a positive and negative root
How can one identify a quadratic formula?
The second difference: after finding the difference between each term, find the difference between those differences. If that value is a constant number, then we have the second difference, and the formula is quadratic.
We can find a by...
finding the second difference/ 2

2a=second difference
We know c because...
it's the y intercept (when x is 0)
We can find b by...
once we a & c, we can plug in for x & y with known points, and solve for b