8adv.MATH.7.C

Determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), and f(bx) for specific values of a, b, c, and d.

Grade 8 (Advanced) · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

Standard Unwrapping

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Vocabulary
graphparent functionf(x) = x^2af(x)f(x) + df(x - c)f(bx)valuesabcd
Skills
  • determine (the effects on the graph of quadratic parent function transformations) #dok2
  • analyze (how changes in a, b, c, and d affect the graph of f(x) = x^2) #dok3
  • describe (the effects of specific transformations on the graph of f(x) = x^2) #dok2
  • predict (the resulting graph after a given transformation) #dok3
Learning Targets
  • I can identify the parent function f(x) = x^2 and its basic graph. #dok1
  • I can describe how multiplying f(x) by a, shifting by c or d, or multiplying x by b transforms the graph. #dok2
  • I can determine the effect on the graph when f(x) = x^2 is replaced by af(x), f(x) + d, f(x - c), or f(bx) for given values. #dok2
  • I can analyze how changing the values of a, b, c, or d affects the shape and position of a quadratic graph. #dok3
  • I can predict the appearance of a quadratic graph after multiple transformations. #dok3
Big Ideas
  • Transformations of quadratic functions change the shape, direction, and position of their graphs.
  • Understanding the effects of parameters in function notation allows students to interpret and predict transformations graphically.
Essential Questions
  • How does changing the value of 'a' in af(x) affect the graph of f(x) = x^2?
  • What impact does shifting by c or d have on the graph of a quadratic function?
  • In what ways does multiplying x by b in f(bx) change the appearance of the graph?
  • Why is it important to understand how each parameter affects the quadratic graph?
  • How can multiple transformations be combined, and what is their cumulative effect on the graph?