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Key Topics of Algebra 1 - Coggle Diagram
Key Topics of Algebra 1
Foundations
Order of Operations
The rule that tells us the sequence in which we should solve an expression with multiple operations. Also known as PEMDAS.
P : Parenthesis
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
Variables, Expressions, Equations, Inequalities
Variables: a placeholder for an unknown quantity. We can usually insert a letter (variable) as a substitute for a number. We can get either a numerical expression or a numerical sentence (which may be true or false). For example, y'all x to the second power +4x, what would x be?
Expressions: An expression is simply just a combination of numbers, variables, and mathematical operations. "An expression is a set of terms combined using the operations +, – , x, or the division symbol. For example 4x+9-81
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Inequalities: a mathematical relationship between two quantities where one is greater or less than the other.
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Functions & Graphing
A function is a relation between a set of inputs and a set of possible outputs, with each input linked to exactly one output.
Slope (types of slopes, slope formula)
Slope: The measure of the steepness and the direction of the line. "The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line."
Types of Slope:
Positive: Indicates that while moving from left to right the line rises. Also signifies that when x increases, so does y.
Negative: Indicates that while moving from left to right the line falls. Also signifies that when x increases, y decreases.
Undefined: The value of the run is zero. (P.S. the slope of a vertical line is undefined.)
Zero: The rise is zero, and thus applying the rise over run formula we get the slope of the line as zero.
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Defining Functions (Domain, Range, Input, Output)
Range: The range of a function is the complete set of all possible output values (often known as values) in terms of the domain.
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Intercepts (x-intercept, y-intercept): Points where a graph touches or crosses the axis
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Quadratic Functions
Quadratic functions graphically, they are represented by a parabola. A quadratic function is a “polynomial function of degree 2.”
The Discriminant (b2−4ac): The Discriminant of a quadratic equation is represented by b2-4ac. It determines the number and type of solutions in a quadratic equation. Something to remember is that when the discriminant is positive there are two solutions but when it is zero there is one repeated solution.
When solving an Quadratic equation you must know about the standard form. The standard form is of the form f(x) = ax2 + bx + c, where a, b, and c are real numbers with a ≠ 0.