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Dmitry_Shevchenko [17]
4 years ago
7

Which graph shows line symmetry about the y-axis?

Mathematics
1 answer:
blsea [12.9K]4 years ago
7 0

Given function is

Now question says to find the graph that shows the axis of symmetry for the given function.

Graph is missing but I can help you to find the correct graph.

Given equation is in the vertex form whose formula is given by

Comparing given function with above formula, we get:

a=1, h=2 and k=1.

For the vertex formula , we know that axis of symetry is given by equation:

x=h

So for the given function, axis of symmetry will be x=2

Graph of x=2 will be a vertical line crossing x-axis at x=2

So you just need to find the graph from given choices which contains a vertical line crossing x-axis at x=2.

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Answer:

1a) f(x) = -1/3(x + 12)² + 9

1b) f(x) = -1/3x² - 8x - 39

General Formulas and Concepts:

<u>Algebra I</u>

Equality Properties

Expand by FOIL (First Outside Inside Last)

Standard Form: ax² + bx + c = 0

Transformations Graph: f(x) = a(bx - c)² + d

  • a = vertical shrink/stretch
  • b = horizontal shrink/stretch
  • c = horizontal movement left/right
  • d = vertical movement up/down

Step-by-step explanation:

<u>Step 1: Define</u>

Reflected down and vertically stretched by 1/3:   a = -1/3

Shifted vertically by 9 units:   d = 9

Shifted horizontally by -12 units:   c = -12

<u>Step 2: Write Vertex Form</u>

  1. Define:                    f(x) = a(bx - c)² + d
  2. Substitute:              f(x) = -1/3(x + 12)² + 9

<u>Step 3: Write Standard Form</u>

  1. Define:                              f(x) = -1/3(x + 12)² + 9
  2. Expand:                             f(x) = -1/3(x² + 24x + 144) + 9
  3. Distribute -1/3:                  f(x) = -1/3x² - 8x - 48 + 9
  4. Combine like terms:         f(x) = -1/3x² - 8x - 39

And we have our final answers!

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Answer:

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Step-by-step explanation:

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to find out

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solution

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