LINEAR FUNCTIONS
QUADRATIC FUNCTIONS
SYSTEMS OF EQUATIONS
CONCEPTUAL
POTENT POTABLES
100
Find the function, in slope-intercept form, which passes through (2,5) and (-3,15)
y = -2x + 9
100
Write the factored form of y = 18x^2 + 54x
y = 18x(x+3)
100
State the coordinate point which satisfies the following system of equations: x - y = 3 7x - y = -3
(-1, -4)
100
What is point-slope form? What does each variable represent?
y - y1 = m(x - x1)
100
Solve for D: A - B = (C+D)/2
D = 2A - 2B - C
200
Find a function, in point-slope form, which passes through (6,-2) and (0, 6)
y + 2 = -3/4 (x - 6) OR y - 6 = -3/4 (x - 0)
200
Factor the following trinomial: 2x^2 + 3x - 14
(2x + 7)(x - 2)
200
Solve the following system of equations using elimination and state the solution as a coordinate point: 5x + 4y = -14 3x + 6y = 6
(-6, 4)
200
What is standard form of a quadratic? What does each variable represent?
y = ax^2 + bx + c
200
Solve the following inequality: (1/2)(x - 5) < x - 2
x > -1
300
Which of the following functions represents the table below: x -1 1 3 y 2 16 30 A. 7x + 10 B. y - 16 = 7(x - 1) C. 7x + 9y = 0
B Slope Intercept Form --> y = 7x + 9 Point-Slope Form --> y - 16 = 7(x-1) Standard Form --> 7x - y = -9
300
What are the x-intercepts of the following function: f(x) = 2x^2 + 6x - 108
(-9,0) and (6,0)
300
A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back upstream took 70 hours. What is the speed of the boat in still water and what is the speed of the current?
IN STILL WATER - 12 MPH CURRENT - 9 MPH
300
Find the mistake: x^2 - 3x + 2 = 7 (x-1)(x-2) = 7 x-1 = 7 OR x-2=7 x=8 x=9 The x-intercepts are (8,0) and (9,0)
The trinomial must be set equal to 0 in order to find x-intercepts
300
Simplify the following with no negative exponents (2x)^2 * y^3 * x^(-4)
(4y^3)/(x^2)
400
What is the rate of change AND x-intercept of the following linear function: 24x + 14y = 7
Rate of Change --> Slope --> -12/7 X-Intercept --> (7/24, 0)
400
Start with a square. Triple its base and increase its height by 4. The resulting rectangle's area is 110 square units larger than the area of the original square. What are the dimensions of the square AND what are the dimensions of the new rectangle?
SQUARE - 5 x 5 RECTANGLE - 15 x 9
400
Brenda's school is selling tickets to a musical. On the first day of ticket sales, the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day, selling 8 senior citizen tickets and 5 child tickets. How much did each ticket cost?
SENIOR CITIZEN TICKET - $4 CHILD TICKET - $7
400
Find the two mistakes, then solve correctly: -4(x-3) > 3x - 5x +6 -4x - 3 > -2x + 6 -2x > 9 x > -9/2
MISTAKES: 1. Did not distribute -4 to -3 2. Did not flip inequality sign when dividing by negative CORRECT ANSWER: x < 3
400
Simplify the following with no negative exponents: (2x^2 * 5x^5 * y^(-3)) / (5x^a * y^1)
5x^(7-a) / y^4
500
Find the function, in slope-intercept form, which passes through the points (2, 3/2) and (7/2, 5)
y = (7/3)x - 19/6
500
A cardboard box has a height of 2 inches and a volume which is 6 times its length. The length of the box is one inch greater than its width. What are the dimensions of the box AND what is the volume of the box?
DIMENSIONS - 2 in x 5 in x 6 in VOLUME - 30 cubic inches
500
The difference in the digits of a certain two digit number is 3. Reversing those digits decreases the number by 27. What is the original number?
36
500
Why is any number raised to the power of 0 equal to 1?
EXAMPLE: 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16 If you were to follow this pattern backwards and divide by 2 as you subtract 1 from the exponent, you would find 2^0 must be equal to 2/2 which is equal to 1
500
Solve the following system of equations. State your solutions as coordinate points: x^2 + y^2 = 26 x - y = 6
(5, -1) AND (1, -5)
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