Page 2: Finding Key Points of Quadratic Functions

This page details the process of finding important points and characteristics of quadratic functions, particularly focusing on the vertex and y-intercept.

Vocabulary: The vertex (h,k) represents the highest or lowest point of a quadratic function.

Definition: The axis of symmetry is a vertical line that passes through the vertex, given by x = -b/2a.

Example: For f$x$ = 3x² - 6x + 5:

• Vertex calculation: h = -$-6$/(2(3)) = 1
• k = f(1) = 2
• Therefore, vertex is (1,2)

Page 3: Graphical Analysis of Quadratic Functions

This page explores the graphical representation of quadratic functions and their key characteristics.

Highlight: The domain of a quadratic function includes all real numbers, while the range depends on whether the parabola opens up or down.

Example: For f$x$ = 3x² - 6x + 5:

• Vertex: V(1,2)
• Axis of symmetry: x = 1
• y-intercept: (0,5)
• Range: [2,∞)

Page 4: Zeros and Additional Features

This page covers the concept of zeros (x-intercepts) and provides additional practice with vertex calculations.

Definition: A zero of a function is an x-value that makes f$x$ = 0, also known as an x-intercept.

Example: For f$x$ = x² - 4x + 3:

• x-intercepts: (1,0) and (3,0)
• y-intercept: (0,3)
• Vertex: $2,-1$

Highlight: The vertex formula h = -b/2a is consistently used throughout different examples to find the turning point of quadratic functions.

Page 1: Introduction to Quadratic Functions

This page introduces the fundamental concepts of quadratic functions in standard form. The content focuses on identifying key components and evaluating functions at specific points.

Definition: A quadratic function in standard form is written as f$x$ = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Example: For the function f$x$ = 3x² - bx + 5:

• a = 3
• b = -b
• c = 5

Highlight: Function evaluation is demonstrated through calculating f(0) = 5, f(1) = 2, and f$-1$ = 14.