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Linear Functions
Systems of Equations
Quadratic Functions
Matrices
Polynomial Functions
100
Define a linear function
Any function that can be written in the form y = mx+b, where m and b are real constants.
100
Define a system of equations
Two or more equations that are simultaneously true.
100
Define "quadratic function"
Quadratic function is a function that has degree 2. OR Quadratic function is a function of the form y = ax^2+bx+c, where a is not equal to 0.
100
What is a matrix?
A rectangular array of numbers
100
What is a polynomial function?
A polynomial function is the sum of one or more monomials with real coefficients and nonnegative integer exponents.
200
Is x=2 a linear function? What about y = 2? Explain.
No and yes. (Cannot and can be written as y = mx+b, also the first one fails the vertical line test.)
200
Sketch the graphs of a system of equations that has 1 solution.
Two (or more) lines that intersect at 1 point.
200
A quadratic function has how many roots? Of what type? List all possibilities.
1 real, or 2 real, or 2 complex
200
In an m by n matrix, m is the number of ____ and n is the number of _____.
Row, column.
200
The degree of -5x^2 + 3x^4 -7x is...
4
300
Near the top, Mt. Everest goes up by 20 meters for every 9 meters in the horizontal. What is the slope of Mt. Everest, to the nearest tenth?
2.2
300
Find all solutions of the system of equations: x+y=3, 2y-6= -2x How many solutions are there?
y = 3-x (infinitely many)
300
When is factored form more useful than vertex form? Explain in full sentences.
When we know the roots and want to create a parabola going through them, factored form is more useful.
300
List 3 real-world applications of matrices (outside of math class).
Airline databases to allow people to buy plane tickets; Amazon.com client databases, keeping track of what you bought; Numerical calculations on graphing calculators.
300
Draw a 5th-degree polynomial with a negative leading coefficient and only 3 real roots.
A graph to be drawn on the board.
400
Given a line through (4, -2) with a slope of -1/4, create an equation for the line perpendicular to the original one, going through the same point.
4(x-2)=y+3
400
How many solutions does the system 6x+y = 7 and 3x+0.5y = 4 have? Explain how you know.
None, since the second equation's left side is the match of the first up to a factor of 2, but the right side isn't.
400
In vertex form, h is the x-coordinate of the vertex. Explain why vertex form has a (x-h)^2 term, instead of (x+h)^2.
The lowest value a square can have is 0, which happens at the vertex. If x = h, (x-h)^2 will be 0, but (x+h)^2 will not.
400
Multiply [ 3 1 0] by | 4 2 | |6 0 | |-2 1 |
[18 6]
400
Give 3 examples of polynomials in the real world, outside of math class.
Calculating profits at a company Calculating dimensions that minimize cost Creating rollercoasters
500
You and your friends go to a sushi restaurant. The restaurant has a promotion: either you pay half of n^2, where n is the number of pieces of sushi you order, or you pay 3 dollars per piece, plus a $5 flat fee. For which n value does the linear function start to cost less than the quadratic one? Explain how you know.
By graphing or solving algebraically, n = 8 starts being cheaper with the linear option.
500
Emily, Poliana and Brian have a doughnut party. Together, Emily and Poliana ate 7 doughnuts, while Poliana and Brian ate 14 doughnuts, and Emily and Brian had 13 doughnuts together. How many doughnuts did the 3 kids eat altogether?
17
500
Write a quadratic equation that could model a bridge that stretches from x = 0 to x = 100 m and that is no more than 50 meters tall.
Answers will vary, but possibilities include -1/50*x(x-100)
500
Find the inverse of the matrix [ 1 3] [ 2 -1]
1/7 [-1 -3] [-2 1]
500
When deciding the end behavior of a function like, for example, x^3 - 100x, we look at the leading term only. So we say that on the negative end, the function will be negative. But if we put in, for example, x = -5, the function will come out to be positive. How can that be?
The function may have a different sign for a while, but eventually, the higher power would win out.