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37 Cards in this Set
- Front
- Back
- 3rd side (hint)
standard form
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y = ax^2 + bx + c
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quadratic term
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ax^2 - to the 2nd degree
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linear term
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bx - to the 1st degree
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constant
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c - no variables
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vertex form
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a(x-h)^2 + k
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parabola
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graph of quadratic equations
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vertex (in terms of graph)
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(LOS, min/max y-value)
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vertex (in terms of vertex form)
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(h, k)
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factoring
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finding an equivalent expression to an expression that is a product of expressions
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scaler factoring
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combine common term factors among terms and group other term factors
e.g. ax^2 + bx → x(ax + b) |
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greatest common factor
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the product of scaler factoring
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prime solution
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solution is not factorable
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perfect square trinomial
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equal binomials squared
A^2 + 2AB + B^2 = ? |
(A+B)^2
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difference of squares
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A^2 - B^2 = ?
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(A+B)(A-B)
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zero product rule
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AB = 0
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sum of cubes
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(A+B)(A^2 - AB + B^2) = ?
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A^3 + B^3
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difference of cubes
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(A-B)(A^2 + AB + B^2) = ?
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A^3 - B^3
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primary and secondary root
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primary = positive root from solution of radical
secondary = negative root from solution of radical |
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multiplication property of radicals
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√(ab) = √a √b
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If the index is higher than the exponents of your radicand (as long as powers are prime), the solution is _?
e.g. ^4√(5^3) |
simplified
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addition of like radicals
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a√x + b√x = (a+b)√x
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quotient rule for radicals
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√(a/b) = √a / √b
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A fractional radicand or radical denominator is _?
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improper
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x^-a = ?
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1 / x^a
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Move the term to the bottom and make it positive.
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1 / x^-a = ?
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x^a
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Move the term to the top and make it positive.
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conjugates
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writing the sum of two terms as difference or writing the difference of two terms as a sum
e.g. √a + √b = conjugate of √a - √b |
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imaginary unit
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i
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(imaginary #)(imaginary #) = ?
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real number
√-9 x √-16 = √144 = 12 |
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complex numbers
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have real and imaginary parts
A + Bi |
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1) i^1 = ?
2) i^2 = ? 3) i^3 = ? 4) i^4 = ? |
1) i
2) -1 3) -i 4) 1 |
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square root property
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take square root of both sides of equation after squared variable is isolated
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A^2 - 2AB + B^2 = ?
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(A-B)^2
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4 methods to solve quadratic equations
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1) table of values
2) factoring 3) completing the square 4) quadratic formula |
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quadratic formula
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x = (-b +/- √(b^2-4ac))/2a
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discriminant
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b^2 - 4ac
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1) discriminant < 0
2) discriminant = 0 3) discriminant > 0 |
1) no real roots
2) 1 real root 3) 2 real roots |
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using a to find two extra points
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(x +/- 1, y + a)
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