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)

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,∞)

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.

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.