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Quadratic Functions Key features

Jane Jang

Created on October 19, 2025

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Transcript

Quadratic Functions Key features

LEARNING TARGETI CAN LEARN KEY FEATURES OF QUADRATIC FUNCTIONS.
3 FORMS OF QUADRATIC FUNCTIONS

click on each to learn more

STANDARD

VERTEX

INTERCEPT

KEY Characteristics

AXIS OF SYMMETRY(AOS)
CONCAVEUP or DOWN
X-INTERCEPT
Y-INTERCEPT
VERTEX

HERE IS AN EXAMPLE OF IDENTIFYING CHARACTERISTICS OF QUADRATICS!

WANT TO PRACTICE?CLICK HERE
NEED MORE HELP?CLICK HERE
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WHAT DO YOU NOTICE ABOUT THE AVERAGE RATE OF CHANGE (AROC) FOR EACH INTERVAL?

STANDARD FORM

EXAMPLE

WHAT DO WE KNOW?

  • a = 2
  • b = 3
  • c = -4

  • Concave Up
    • if a is (+), graph is concave up
    • if a is (-), graph is concave down
  • Y-INTERCEPT = (0 , -4)

VERTEX FORM

VERTEX = (-h, k) only h is opposite

EXAMPLE

WHAT DO WE KNOW?

  • Vertex = (-3, -4)
  • Axis of Symmetry (AOS)
x = -3

  • Concave Up
    • if # in front of parenthesis is (+), graph is concave up
    • if # in front of parenthesis is (-), graph is concave down

INTERCEPT FORM

x-intercepts (OPPOSITES)

EXAMPLE

WHAT DO WE KNOW?

  • x - intercepts (also known as roots, zeros, or solutions)
    • (-4, 0)
    • (-2, 0)
***REMEMBER: x-intercept is when y = 0***