Unit 5: Quadratic Functions
Vocabulary
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Monomial- is a number, a variable, or a product of numbers with whole-number exponents.
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Polynomial- is a monomial or sum of monomials
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Binomial- is a polynomial with two terms.
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Trinomial- is a polynomial that has three terms.
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Difference of Two Squares: a squared (multiplied by itself) number subtracted from another squared
number. It refers to the identity a2 – b2 = (a + b) ( a – b)
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Perfect Square Trinomial: A trinomial that factors into two identical binomial factors.
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Quadratic Equation: An equation of degree 2, which has at most two solutions.
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Quadratic Function: A function of degree 2 which has a graph that “turns around” once, resembling an
umbrella-like curve that faces either rightside up or upside down. This graph is called a parabola.
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Parabola- a U shaped curve
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vertex form of a quadratic function- is f(x) = a(x – h)2 + k, where a, h, and k are constants. The vertex
is (h,k)
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Standard Form of a Quadratic Function: ax2+bx +c
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Vertex: The maximum or minimum value of a parabola, either in terms of y if the parabola is opening
up or down, or in terms of x if the parabola is opening left or right.
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Axis of symmetry- is the line through the vertex of the parabola that divides the parabola into two
congruent halves.
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Minimum value- When a parabola opens up, the y value of the vertex is the minimum
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Maximum value- When the parabola opens down, the y value of the vertex is the maximum.
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Quadratic model- a quadratic function that represents a real data set.
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Quadratic Regression- A statistical method to make a quadratic model for a given data set.
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Root/ zero of a function: The x-values where the function has a value of zero.
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Completing the Square: Completing the Square is the process of converting a quadratic equation into a
perfect square trinomial by adding or subtracting terms on both sides.
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Perfect square- an expression that has two identical factors
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Discriminant of a quadratic equation: The discriminant of a quadratic equation of the form o ax +
2
2
bx+ c = 0, a ≠ 0, is the number b – 4ac.
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Nonlinear system of equations- a system in which at least one of the equations is non linear.