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c h a p t e r s i x

Quadratic Functions

general quadratic expression ax^2 + bx + c
quadratic equation ax^2 + bx + c = 0
quadratic function (standard form of a quadratic) f: x --> ax^2 + bx + c
Binomial Square Theorem For all real numbers x and y, (x+y)^2 = x^2 + 2xy + y^2 and (x-y) = x^2 - 2xy + y^2
|-28| = ? 28 (absolute value)
what is the graph of the absolute value function? f(x) = |x| an angle
Graph-Translation Theorem In a relation described by a sentence in xa dn y, the following two processes yield the same graph: (1) replacing x by x - h and y by y - k; (2) applying the translation T*h,k to the graph of the original relation.
graph of the equation y = ax^2 + bx = c is a parabola congruent to the graph of what equation? y = ax^2
Imaginary numbers Square root of a negative number like -100 is 10i. Turn positive and add on imaginary number symbol (i)
i^2 = ? -1
Complex number when a real number and an imaginary number are added. In the form of a + bi
Discriminant Theorem Suppose a, b, c are real numbers with a not equaling 0. Then the equation ax^2 + bx + c = 0 has (i) two real solutions if b^2 - 4ac > 0. (ii) one real solution if b^2 - 4ac = 0. (iii) two complex conjugate solutions if b^2 - 4ac < 0.
Created by: katelesperance