Linear Equations
What is the standard form of a linear equation?
Ax + By = C, where A, B, and C are constants.
What symbol is used to show "less than or equal to"?
≤
What is the general form of an exponential function?
y = a * bx, where a ≠ 0 and b > 0, b ≠ 1.
What is the standard form of a quadratic function?
y = ax2 + bx + c, where a ≠ 0.
What is the order of operations acronym to remember the sequence?
PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
What does the slope of a line represent?
The rate of change or how much y changes for a unit change in x.
When you multiply or divide both sides of an inequality by a negative number, what must you do to the inequality sign?
Reverse (flip) the inequality sign.
In the function y = 3 * 2^x, what is the base and what does it represent?
The base is 2, representing the growth factor.
What shape does the graph of a quadratic function make?
A parabola.
What property states that a + b = b + a?
Commutative property of addition.
How do you find the slope given two points on a line?
Subtract the y-values and divide by the difference of the x-values: (y2 - y1) / (x2 - x1). OR Rise/Run
How is the solution to a linear inequality represented on a number line?
An arrow is draw to the side where solutions lie.
What is the y-intercept of any exponential function y = a * bx?
The y-intercept is a (when x = 0).
How does the value of "a" affect the parabola?
If a > 0, it opens upward; if a < 0, it opens downward.
What is the difference between an expression and an equation?
An expression has no equals sign; an equation does.
What is the meaning of the y-intercept in the equation y = mx + b?
The point where the line crosses the y-axis (when x = 0).
What does a dashed line versus a solid line mean when graphing linear inequalities?
Dashed line means the inequality is < or > (not including the line), solid line means ≤ or ≥ (including the line).
How do you know if an exponential function represents growth or decay?
If the base b > 1, it’s growth; if 0 < b < 1, it’s decay.
How do you find the vertex of a parabola using the formula y = ax² + bx + c?
Use the vertex formula: x = -b/(2a), then plug x back into the equation to find y.
What is the value of any number raised to the zero power (except zero)?
1
How can you tell if two lines are parallel by looking at their slopes?
They have the same slope but different y-intercepts.
When solving a system of linear inequalities, how do you find the solution region?
Graph each inequality and find the overlapping shaded region that satisfies all inequalities.
What happens to the graph of y = a * bx if a is negative?
The graph reflects over the x-axis.
How can you determine the number and type of solutions of a quadratic equation by analyzing its graph?
By looking at where the parabola crosses the x-axis: two points means two real solutions, one point means one real solution, and no points means no real solutions (complex roots).
What is the difference between rational and irrational numbers?
Rational numbers can be written as fractions; irrational numbers cannot.