Unit 3: Parent Functions & Transformations Name

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Unit 3: Parent Functions & Transformations Name: Bell: Homework 5: Vertex Form of a Quadratic Equation Date: ** This is a 2-page documenti Describe the transformation of each function compared to its parent function. 1. f(x) – (x-4 .9 Horizontal shift to the right vertical stretch by a tactor of 2 04 A nits “Reflection aloout the ans. vertical shift up by 9 units Vertical shift dam by 3 units Horizontal Shil 3. f(x) = (x+6) to the left by 4. (x)=-7-7- 1 38 SO T Gunit Reflection about the starit, Vertical compression by a factor vertical shift down by lunft Petro 3 Vertical stretch by 6. f(x) = – 2 (x – 5)² + 2 Hoe right by & fach Reflection about the x-axist Vertical shift up by 2 units Give the vertex and axis of symmetry of each equation/inequality, then graph. 7. /(x) = (x+1)-8 8. S(x) = (x+5)* +5 3. S (x) – 2 factor of 3/27 9.50)=2x-3 10. f()=-3(x-4) +1 -2 lfx=4 +8f1 12./8)= 10-4) -5×24 11. 5 – 2x 1fx>1 13. f(x) > 14. f(x)2 47° -7 15. f(x)

The correct answer and explanation is:

It seems like you’re working on a math worksheet related to quadratic functions in vertex form and their transformations. Here’s a structured explanation of how to approach this type of problem, including a detailed breakdown of transformations, vertex, and axis of symmetry:

Understanding the Vertex Form:

The vertex form of a quadratic equation is:
f(x)=a(x−h)2+kf(x) = a(x-h)^2 + k

  • hh: Horizontal shift (right if h>0h > 0, left if h<0h < 0).
  • kk: Vertical shift (up if k>0k > 0, down if k<0k < 0).
  • aa: Controls the vertical stretch/compression and reflection.
    • If ∣a∣>1|a| > 1: Vertical stretch.
    • If 0<∣a∣<10 < |a| < 1: Vertical compression.
    • If a<0a < 0: Reflection about the x-axis.

Steps for Each Problem:

  1. Identify the Transformations:
    • Compare the given equation with the parent function f(x)=x2f(x) = x^2.
    • Note any horizontal shifts (hh), vertical shifts (kk), and changes to the coefficient (aa).
  2. Find the Vertex:
    • The vertex is (h,k)(h, k).
  3. Determine the Axis of Symmetry:
    • The axis of symmetry is the vertical line x=hx = h.
  4. Graph the Function:
    • Plot the vertex.
    • Use the direction of opening (upward if a>0a > 0, downward if a<0a < 0) and the stretch/compression factor to sketch the parabola.

Example Breakdown:

Problem 1: f(x)=2(x−4)2+9f(x) = 2(x – 4)^2 + 9

  1. Transformations:
    • Horizontal shift: Right by 4 units.
    • Vertical stretch: By a factor of 2.
    • Vertical shift: Up by 9 units.
  2. Vertex: (4,9)(4, 9).
  3. Axis of Symmetry: x=4x = 4.

Problem 2: f(x)=−13(x+6)2−1f(x) = -\frac{1}{3}(x+6)^2 – 1

  1. Transformations:
    • Horizontal shift: Left by 6 units.
    • Vertical compression: By a factor of 13\frac{1}{3}.
    • Reflection: About the x-axis (due to the negative aa).
    • Vertical shift: Down by 1 unit.
  2. Vertex: (−6,−1)(-6, -1).
  3. Axis of Symmetry: x=−6x = -6.

For the Writing Portion:

In a 300-word explanation, you would:

  • Describe the significance of the vertex form.
  • Explain how each parameter (aa, hh, kk) affects the graph.
  • Highlight the step-by-step process for analyzing transformations, finding the vertex, and determining the axis of symmetry.
  • Discuss how changes in aa influence the parabola’s shape and orientation.

Would you like further assistance with specific problems or the 300-word explanation?

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