Algebra 1: Chapter 8 Flashcards
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Questions and Answers

What is the average rate of change?

f(b) - f(a) / b - a

What is the axis of symmetry?

A line that divides a plane figure or a graph into two congruent reflected halves

What is an even function?

f(-x) = f(x)

What is intercept form?

<p>f(x) = a(x - p)(x - q) where a ≠ 0</p> Signup and view all the answers

What is the maximum value of a quadratic function?

<p>The y-coordinate of the vertex of the quadratic function f(x) = ax^2 + bx + c, where a &gt; 0</p> Signup and view all the answers

What is the minimum value of a quadratic function?

<p>The y-coordinate of the vertex if a &gt; 0 for y = ax^2 + bx + c</p> Signup and view all the answers

What is an odd function?

<p>f(-x) = -f(x)</p> Signup and view all the answers

What is a parabola?

<p>The U-shaped graph of a quadratic function</p> Signup and view all the answers

What is the vertex form of a quadratic function?

<p>y = a(x - h)^2 + k</p> Signup and view all the answers

What is the vertex of a parabola?

<p>The highest or lowest point on the graph</p> Signup and view all the answers

What is a zero of a function?

<p>An x-value that makes the function equal to 0</p> Signup and view all the answers

Study Notes

Average Rate of Change

  • Calculated using the formula: ( \frac{f(b)-f(a)}{b-a} )
  • Represents how a function changes on average over an interval.

Axis of Symmetry

  • A line that bisects a figure or graph into two identical halves.
  • Critical in analyzing the shape of parabola graphs.

Even Function

  • Defined by the property: ( f(-x) = f(x) )
  • Symmetrical about the y-axis, meaning both sides of the graph mirror each other.

Intercept Form

  • A quadratic function expressed as ( f(x) = a(x - p)(x - q) ) where ( a \neq 0 )
  • Represents the function's x-intercepts at points ( p ) and ( q ).

Maximum Value

  • The highest y-coordinate of a quadratic function's vertex when ( a > 0 ).
  • Important for determining the peak value of upward-opening parabolas.

Minimum Value

  • The lowest y-coordinate of a quadratic function's vertex when ( a > 0 ).
  • Critical for defining the lowest point on upward-opening parabolas.

Odd Function

  • Characterized by the relation: ( f(-x) = -f(x) )
  • Exhibits rotational symmetry about the origin.

Parabola

  • U-shaped graph representing quadratic functions.
  • Can open upward or downward, depending on the coefficient ( a ).

Vertex Form of a Quadratic Function

  • Written as ( y = a(x - h)^2 + k )
  • Provides crucial information about the vertex's position and the graph's direction.

Vertex of a Parabola

  • The point at which the parabola reaches its maximum or minimum value.
  • Essential in graphing and understanding the behavior of quadratic functions.

Zero of a Function

  • An x-value that causes the function to equal zero.
  • Indicates the points where the graph intersects the x-axis, also known as roots or x-intercepts.

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Test your knowledge on key concepts from Algebra 1, Chapter 8 with these flashcards. You'll encounter terms like average rate of change, axis of symmetry, and even function. Perfect for reviewing and reinforcing your understanding of quadratic functions and their properties.

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