Algebra 1 EOC FL study guide
Domain
Input or X-values
Absolute Value Inequalities
Less Than= forms "and" compound inequality (Less Th-AND) |x|<8 -8<x<8 Greater Than= forms "or" compound inequality (Great-OR Than) |x|>10 x<-10 or x>10
Foil
Multiply first, outer, inner, and last terms
Range
Output or Y-values
Perpendicular Lines
Two lines with opposite reciprocal slopes Ex: 3 and -1/3
Parallel Lines
Two lines with the same slope
Discriminant
Used to determine the number of solutions for a quadratic equation Positive: 2 solutions Zero: 1 solution Negative: no solutions b²-4ac
Vertical Line Test
Used to determine whether a graphed relation is a function 1) Draw a vertical line through every point on the graph 2) If each vertical line drawn intersects only one point, i is a function 3) If any vertical line drawn intersects more than one point, it is not a function
X-Intercept
Where the graph crosses the x axis (x,0) Set y=0 to find
Y-Intercept
Where the graph crosses the y axis (0,y) Set x=0 to find
Zero of a Function
X-intercept (find x-value when y or f(x) equals zero)
Exponent Rules
a^m × a^n=a^m+n Ex: 4³ × 4⁶=4⁹ a^m/a^n=a^m-n Ex: 3¹⁰/3⁴=3⁶ (a^m)^n=a^mn Ex: (6²)⁵=6¹⁰ (ab)^m=a^m × b^m Ex: (2×5)³=2³×5³ (a/b)^m=a^m/b^m Ex:(¾)²=3²/4² a⁰=1 Ex: 8⁰=1 a^-n= 1/a^n Ex: 5^-3=¹/₅³ a^m/n=n√a^m Ex: 25³/²= (√25)³
Arithmetic Sequence
a_n=a₁ + (n-1)d n= nth term a₁=1st term d= common difference (+ or - pattern)
Geometric Sequence
a_n=a₁ × r^n-¹
Zeros of a Quadratic Function
x-intercepts on the parabola
Vertical Line
x=a All points have the same x value
Graphing Inequalities on a Number Line
x>a or x<a = Open circle at a Shade in the direction of your solution x≥a or x≤a = closed circle at a Shade in the direction of your solution
Point-Slope Form
y-y₁=m(x-x₁) m=slope (x₁,y₁)=point on the line
Quadratic Function
y=ax²+bx+c Graph is a parabola or u shaped If a is positive, parabola faces up If a is negative, parabola faces down Use x=-b/2a to find the axis of symmetry and the x coordinate of the vertex
Horizontal Line
y=b All points have the same y value
Direct Variation
y=kx where k= constant of variation (slope of line) k=y/x The graph is a line that always passes through the origin
Slope-Intercept Form
y=mx + b m=slope b=y-intercept
Absolute Value Equations
|x|=4 x=4 or x=-4 |x|=6 x= no solution
Slope Formula
Δy/Δx=y₂-y₁/x₂-x₁
Opposites
A and -A Ex: -5 and 5
Rational Number
Any number that can be written as a fraction (Includes proper/improper fractions, mixed numbers, terminating decimals, repeating decimals with a pattern, integers, and whole numbers)
Irrational Number
Any number that cannot be written as a fraction (Includes only repeating decimals with no pattern)
Standard Form
Ax+Bx=C A, B, & C must be integers
Special Cases
If both variables cancel out, the answer is either no solution (false statement) or many solutions (true statement)
Squaring a Binomial (Special Product)
(a+/_b)²=a²+/-2ab+b²
Sum and Difference (Special Product)
(a+b)(a-b)=a²-b²
Integers
-3, -2, -1, 0, 1, 2, 3, ...
Whole Numbers
0, 1, 2, ...
Graphing a Linear Inequality
1) Graph the boundary line (≥ or ≤ = solid line, > or < = dashed line) 2) Pick a test point to determine which half of the graph to shade If solving a system of linear ineqalities, the solution is where the shaded regions overlap
Methods of Solving a Linear System
1) Graphing (solution= where the two lines intersect) 2) Substitution (use if one equation is solved for x or y) 3) Elimination (use if both equations are in standard form
Methods for Solving a Quadratic Equation
1)Factoring:Equation must be set equal to zero before factored 2)Square roots: only used if b-term is missing (ax²+c=0) 3) Completing the square: Equation must be in the form ax²+bx=c; you need to factor out the leading coefficient if a≉1 4)Quadratic formula: USed if the equation cannot be factored; you must set the equation equal to zero first X=-b+/-√b²-4ac/2a
Absolute Value
Distance between a number and zero (always positive)
Functions
Each input is paired with exactly one output (no repeating input values)
Exponential Functions
Graph forms a smooth curve that approaches the x axis but never intersects it y=a×b^x where a ≉ 0, b≉1, and b>0
Solving an Inequality
Reverse the inequality sign if you multiply or divide both sides of the inequality by a negative number
