ALG1.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), f(bx) for specific values of a, b, c, and d.

Algebra I · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

Standard Unwrapping

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Vocabulary
graphparent functionf(x) = x²transformationaf(x)f(x) + df(x - c)f(bx)valuesabcdeffects
Skills
  • identify (parent and related quadratic functions) #dok1
  • describe (effects of coefficients and constants on the parent function f(x) = x²) #dok2
  • analyze (the result of replacing f(x) with af(x), f(x) + d, f(x - c), and f(bx)) #dok2
  • predict (changes in the graph of f(x) = x² when a, b, c, or d change) #dok3
  • generalize (patterns for how different transformations affect the graph of f(x) = x²) #dok3
Learning Targets
  • I can identify the parent function f(x) = x² and its graph. #dok1
  • I can distinguish between f(x) = x² and its transformed forms. #dok1
  • I can describe how changing a, b, c, or d in af(x), f(x) + d, f(x - c), or f(bx) affects the graph of f(x) = x². #dok2
  • I can analyze the impact of different values of a, b, c, or d on the graph of the quadratic function. #dok2
  • I can predict what the graph of f(x) = x² will look like after applying multiple transformations. #dok3
  • I can generalize rules for graphing transformations of quadratic functions. #dok3
Big Ideas
  • Transformations systematically alter the graph of the parent quadratic function, affecting its shape, position, and orientation.
  • Understanding how the parameters a, b, c, and d change the graph of f(x) = x² is key to graphing and interpreting quadratic functions.
Essential Questions
  • How does each parameter (a, b, c, d) affect the graph of the parent function f(x) = x²?
  • What types of transformations can be applied to the graph of a quadratic function?
  • Why is it important to analyze the effects of transformations on quadratic functions in real-world contexts?
  • How can the rules for transforming f(x) = x² help us quickly sketch or interpret new quadratic graphs?
  • What patterns can you notice when comparing different transformations of quadratic functions?