Definitions
In a graph, what is an "intercept"?
Where the graph crosses the x- or y-axis
How many outputs exist in a function for each input?
One
The absolute value of 6^2 - 12(5)
26
Evaluate when x= (-3.5) and y= 12
2y - 3x
34.5
solve the system 2x+y=6 y-2x=2
(1,4)
What are the roots of a quadratic equation?
The solutions or the x-intercepts or the zeroes
Rewrite the in slope intercept form and find the intercepts. 3x-2y=12
y=3/2(x)+6 xint.=4 yint.=-6
Identify the pattern and find the next number in the sequence: 1, 2, 4, 8, 16, ?
X2, 32
Simplify (ab)^c
(a^c)(b^c)
The three strategies to solving systems of equations
elimination, graphing, substitution
Define axis of symmetry, and state the formula for finding the axis of symmetry in a quadratic function.
Axis of Symmetry: where the graph is cut in half. Creates a mirror image over the axis. x=-b/(2a)
Find the zeros of the function f(x)= x^2+2x-35
x=-7 x=5
What is the effect on the graph of y=(x-2)^2+7 if the -2 is changed to 5
the graph would be translated 7 units left
Factor x^2-36
(x-6)(x+6)
How can you classify a system by its number of solutions?
1 solution: Independent and consistent No solution: inconsistent Infinitely many solutions: Dependent and consistent
What is the discriminant of a quadratic and what does it represent?
b^2-4ac represents the number of solutions. positive: 2 real solutions zero: 1 real solution negative: 2 imaginary solutions
Write a quadratic function in standard from "ax^2+bx+c" with zeros -5 and 3
f(x)=x^2+2x-15
an office is printing 2400 copies using two printers. If printer A prints three times as many copies as printer B. How many copies did each printer produce?
Printer A: 1800 Printer B: 600
Factoring of: 2x^2 + 7x - 4 = 0
(2x-1)(x+4)
Classify the system and determine the number of solutions 5x-6y=12 -15x+18y=-24
Inconsistent, no solution
Define slope, and give the formula for finding the slope of a line.
slope is a ratio: rise/run it determines the steepness of the graph. m(slope)=(Y2-Y1)/(X2-X1)
Find the minimum or maximum value of f(x)= -x^2-4x+8 and state domain and range
max (-2,12) Domain: all real numbers Range: y <=12
The difference between an expression and an equation
Equations have an equal sign
Simplify (18x^5y^2)/ (12x^3y^7)
(3x^2)/ (2y^5)
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?
1,500 children, 700 adults