Questions and Answers
What does the 'm' represent in the linear equation form y = mx + b?
A parabola opens downwards if the coefficient 'a' in the equation y = ax² + bx + c is greater than zero.
False
What is the formula to find the xcoordinate of the vertex of a parabola?
x = b/(2a)
In standard form of an exponential function, $y = ab^x$, b represents the ______ factor.
Signup and view all the answers
Match the following types of slopes to their descriptions:
Signup and view all the answers
When graphing the line for an inequality such as y < mx + b, what type of line is used?
Signup and view all the answers
In a Cartesian plane, Quadrant II is characterized by x < 0 and y < 0.
Signup and view all the answers
What is the shape of the graph of an exponential growth function?
Signup and view all the answers
Study Notes
Graphing
Linear Equations

Form: y = mx + b
 m = slope (rise/run)
 b = yintercept (where the line crosses the yaxis)

Slope:
 Positive slope: line rises from left to right
 Negative slope: line falls from left to right
 Zero slope: horizontal line
 Undefined slope: vertical line

Graphing Steps:
 Identify slope and yintercept.
 Plot the yintercept on the graph.
 Use the slope to find another point.
 Draw the line through the points.
Quadratic Functions

Form: y = ax² + bx + c
 a, b, and c are constants; a ≠ 0

Parabola:
 Opens upwards if a > 0, downwards if a < 0.

Vertex:
 The highest or lowest point of the parabola.
 Formula: x = b/(2a) to find the xcoordinate of the vertex.
 Axis of Symmetry: x = b/(2a)

Graphing Steps:
 Find the vertex and axis of symmetry.
 Identify additional points by choosing xvalues.
 Plot the points and draw the parabola.
Graphing Inequalities

Types:
 Linear inequalities (e.g., y < mx + b)
 Quadratic inequalities (e.g., y < ax² + bx + c)

Graphing Steps:
 Graph the corresponding equation as if it were an equality.
 Use a dashed line for < or >; solid line for ≤ or ≥.
 Shade the region that satisfies the inequality.
 Test a point in the shaded region to confirm.
Coordinate Systems

Cartesian Plane:
 Composed of two perpendicular axes: xaxis (horizontal) and yaxis (vertical).
 Origin: (0,0), where the axes intersect.

Quadrants:
 Quadrant I: (x > 0, y > 0)
 Quadrant II: (x < 0, y > 0)
 Quadrant III: (x < 0, y < 0)
 Quadrant IV: (x > 0, y < 0)
 Point Notation: (x, y), where x is the horizontal position and y is the vertical position.
Exponential Growth

Form: y = ab^x
 a = initial value, b = growth factor (b > 1)

Characteristics:
 Rapid increase as x increases.
 Graph passes through the point (0, a).
 Asymptote: The xaxis (y = 0) is a horizontal asymptote.

Graphing Steps:
 Identify the initial value (a) and growth factor (b).
 Calculate y for a few key xvalues (e.g., 1, 0, 1, 2).
 Plot the points and draw a smooth curve through them.
Linear Equations
 Expression follows the form y = mx + b, where m is the slope and b is the yintercept.
 Slope (m) indicates the steepness and direction of a line:
 Positive slope: line ascends from left to right.
 Negative slope: line descends from left to right.
 Zero slope: indicates a horizontal line.
 Undefined slope: represents a vertical line.
 Steps for graphing include identifying the slope and yintercept, plotting the yintercept, using the slope to find additional points, and drawing the line.
Quadratic Functions
 Formulated as y = ax² + bx + c, with coefficients a, b, and c; a must not equal zero.
 The parabola formed opens upwards if the leading coefficient (a) is positive and downwards if negative.
 The vertex, which is the peak or lowest point, can be found using x = b/(2a).
 The axis of symmetry of the parabola is also at x = b/(2a).
 For graphing quadratics, identify the vertex and axis of symmetry, choose xvalues to find additional points, and plot to complete the parabola.
Graphing Inequalities
 Includes linear inequalities (e.g., y < mx + b) and quadratic inequalities (e.g., y < ax² + bx + c).
 First, graph the corresponding equation like an equality.
 Use a dashed line for strict inequalities (< or >) and a solid line for inclusive inequalities (≤ or ≥).
 Shade the area representing solutions to the inequality and confirm by testing a point from the shaded region.
Coordinate Systems
 The Cartesian plane features two intersecting axes: the xaxis (horizontal) and yaxis (vertical).
 The point of intersection is the origin (0,0).
 Divided into four quadrants, characterized as:
 Quadrant I: x > 0, y > 0
 Quadrant II: x < 0, y > 0
 Quadrant III: x < 0, y < 0
 Quadrant IV: x > 0, y < 0
 Points are denoted in the format (x, y), indicating horizontal and vertical positions respectively.
Exponential Growth
 Expressed in the form y = ab^x, where a represents the initial value and b is the growth factor; b must be greater than 1.
 Characterized by rapid increases in value as x increases.
 The graph intersects the yaxis at the point (0, a) and has a horizontal asymptote at y = 0 (the xaxis).
 Graphing requires identifying the initial value and growth factor, determining y for several key xvalues, and plotting these points to draw a smooth curve.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers the essentials of graphing linear equations and quadratic functions. You'll learn about the formulas, slopes, intercepts, and how to identify key features like the vertex and axis of symmetry. Test your understanding of these foundational concepts in algebra!