Chapter 2
Systems of Equations and Inequalities
Quadratic Functions and Equations
5-5 and Beyond
Personal Math Growth
100
Two values that are not equal.
What is an inequality? Annotated solution: Example: y>1/2x-3
100
A set of two or more equations that use the same variables.
What is a system of equations? Annotated solution: Example: -2x=3y=8 and 3x-y=-5
100
A function that can be written in the form f(x)=ax²+bx+c, where a does not equal 0.
What is a quadratic function? Annotated solution: Example: y=2x²-5x-12 is a quadratic function, because it can be written in the standard form of f(x)=ax²+bx+c.
100
If ab=0, then either a=0 or b=0.
What is the zero-product property? Annotated solution: The zero-product property says that if ab=0, then either a or b is equal to 0. So, if the equation (x-5)(x+3)=0, then then either (x-5)=0 or (x+3)=0.
100
Tessa's initial reaction to math.
What is frustration?
200
y=mx+b
What is slope-intercept form? Annotated solution: Example: y=9x+7.5
200
Classification of a system of coinciding lines.
What is dependent? Annotated solution: A system that graphs as coinciding lines (or the same line), is classified as dependent because all points are shared.
200
The graph of a quadratic function.
What is a parabola? Annotated solution: When you graph a quadratic function, you will get a parabola. It's shaped like a "U" or an upside-down "U". An axis of symmetry separates it down the middle.
200
An imaginary number whose square is -1.
What is "i"? Annotated solution: The imaginary number, "i", is equal to the square root of -1. Imaginary numbers are numbers in the form of a+bi, where "a" and "b" are real numbers and b is not 0.
200
An activity normally done before an exam, that may increase grades.
What is studying?
300
In a relation, each element of the domain is paired with exactly one element of the range.
What is a function? Annotated solution: Example f(x)=0
300
Solving systems by substituting the expression of one equation for the y value of the other.
What is substitution? Annotated solution: The system of y=2x-7 and 4x+3y=2 can be solved by substitution. This would be done by solving the equation 4x+3(2x-7)=4. The expression for "y" was substituted for the variable in the other equation.
300
Factoring of x²-17x+72
What is (x-9)(x-8)? Annotated solution: ac=72 and b=-17 x²-8x-9x+72 x(x-8)-9(x-8) (x-9)(x-8)
300
The process of finding the last term of a perfect square trinomial.
What is completing the square?
300
A key element to succeeding in any class, without it, one feels no need to pay attention or work hard.
What is motivation?
400
y=3x+4 and y=3x+6
What are the equations of parallel lines? Annotated solution: The equations of parallel lines have the same "m" value, or slope, but the "b" value is different.
400
A system that has one unique solution.
What is an independent system? Annotated solution: Example: x-y=5 and y+3=2x is an independent system.
400
a(x-h)²+k
What is the vertex form of a quadratic function? Annotated solution: Vertex form is where (h,k) is the vertex. Example: the vertex form of y=2x²+10x+7 is y=2(x+2.5)²-5.5
400
x=[-b ± √(b^2 - 4ac)] / 2a
What is the quadratic formula? Annotated answer: Not sure how to put an annotated answer here. This is definitely the quadratic formula.
400
A good way to study and improve understanding. Also raises your work-study habits grade.
What is homework?
500
DOUBLE JEOPARDY-- A point where a function meets its maximum or minimum.
What is a vertex? Annotated solution: Example: the vertex of the equation y=-0.5(x-2)²+3 is (2,3)
500
A system whose solutions can be shown as the intersections of planes.
What is a three-variable system? Annotated solution: A three-variable system can be shown as the intersections of planes. For example, when the planes intersect at one common point, there is one solution. When the planes intersect at all point along one line, there is infinite solutions. And when no point is on all three planes, there is no solution.
500
FINAL JEOPARDY-- The equation for the axis of symmetry.
What is -b/2a? Annotated solution: Finding the axis of symmetry for y=3x²+12x+8. -12/2(3) -12/6 The axis of symmetry is -2.
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