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Advanced Algebra

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|x| = {x, for x>0 or x=0}
{-x, for x<0}

for all real numbers x, the square root of x-squared is equal to |x|
absolute value
in the vertex form, if a<0, then the parabola opens ____ and the y coordinate of the vertex is the minimum y-value. If a>0, then the parabola opens ____
up, down
the image of the parabola y=ax-squared under the translation Th,k is the parabola with the equation y-k=a(x-h)-squared.
corollary
in a relation described by a sentence in x and y, the following two processes yield the same graph:
1. replacing x by x-h and y by y-h
2. applying the translation (slide) Th,k to the graph of the original relation
Graph Translation Theorem
What is the domain of a quadratic function?
the set of real numbers.
what is the y intercept of the quadratic formula?
f(0)=c, c is the y-intercept when x=0.
the graph of the equation ______ is a parabola congruent to the graph of ______

the graph of every quadratic formula is a parabola
y=ax-squared+bx+c, y=ax-squared
vertex(es)
(h,k)
vertex form of a quadratic function
y-k=a(x-h)squared
1. ax-squared+bx+c
standard quadratic expression
how do you complete the square on x-squared+bx?
add (0.5b)-squared
what number should be added to x-squared+10x to make a perfect square trinomial?
25
quadratic formula
x= (-b + or - the square root of b-squared - 4ac)/2
the term which refers to a square root of a negative number.

i=square root of -1
imaginary number
the ______ of a+bi is a-bi, and it allows us to divied complex numbers.
complex conjugate
The ______ determines the nature of the solutions to a quadratic function. The ______ is b-squared - 4ac
discriminant
A ______ is a number of the form a+bi, where a and b are real numbers; a is called the real part and b is called the imaginary part

When a real number and an imaginary number are added, the sum is a ______
complex number
If b-squared - 4ac < 0
There are two nonreal solutions
If b-squared - 4ac = 0
there is one real solution
If b-squared - 4ac > 0
there are two real solutions
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