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Describe the transformation of the parent function. f(x) = x^2. Then graph the transformed function 16. f(x) = (x - 1)^2 + 3 17. y = (x + 1)^2 - 3 18. g(x) = 2x^2 19. f(x) = -(x - 1)^2 + 7

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tramserran

Answer: 16) Shifted LEFT 1 unit and DOWN 3 units

               17) Shifted LEFT 1 unit and DOWN 3 units

               18) Vertical stretch by a factor of 2

               19) Reflected over x-axis, shifted RIGHT 1 unit and UP 7 units

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k    where

  • "a" is the vertical stretch
  • -a is a reflection over the x-axis
  • h is the horizontal shift (positive = right, negative = left)
  • k is the vertical shift (positive = up, negative = down)

f(x) = x²

16)  f(x) = (x - 1)² + 3

                    ↓      ↓

                  h= 1    k= 3

           Shifted RIGHT 1 unit and UP 3 units

17) f(x) = (x + 1)² - 3

                    ↓      ↓

                 h= -1   k= -3

           Shifted LEFT 1 unit and DOWN 3 units

18) f(x) = 2(x)²

              ↓    

             a= 2

           Vertical stretch by a factor of 2

19) f(x) = -(x - 1)² + 7

             ↓    ↓      ↓

           a= -1 h= 1  k= 7

           Reflected over x-axis, shifted RIGHT 1 unit and UP 7 units

Rules for the transformations of a parent function are given as,

 If the parent function f(x) = x² is transformed as,

  • Shifted 1 unit left, the image function will be,

        g(x) = (x + 1)²

  • Shifted 1 unit right, the image function will be,

        g(x) = (x - 1)²

  • Shifted 1 units upwards, image function will be,

        g(x) = x² + 1

  • Shifted 1 units downwards, image function will be,

        g(x) = x² - 1

  • Vertically stretched by a factor k,

        g(x) = kx²

  • Inverted about the x-axis,

        g(x) = -x²

With the help of these transformations, following transformed functions will be defined as,

 16). f(x) = (x - 1)² + 3

        Parent function is shifted 1 unit right and 3 units upwards.

  17). y = (x + 1)² - 3

        Parent function is shifted 1 unit left and 3 units left.

  18). g(x) = 2x²

        Parent function is vertically stretched by a factor of 2.

  19). f(x) = - (x - 1)² + 7

        Parent function is inverted about the x-axis, followed by 1 unit shift on the right and 7 units upwards.      

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