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21 The graph of the curve with equation $y = f(x)$ is shown on the grid below - Edexcel - GCSE Maths - Question 22 - 2020 - Paper 2

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21 The graph of the curve with equation $y = f(x)$ is shown on the grid below. (a) On the grid above, sketch the graph of the curve with equation $y = f(-x)$. The... show full transcript

Worked Solution & Example Answer:21 The graph of the curve with equation $y = f(x)$ is shown on the grid below - Edexcel - GCSE Maths - Question 22 - 2020 - Paper 2

Step 1

On the grid above, sketch the graph of the curve with equation $y = f(-x)$

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Answer

To sketch the graph of y=f(−x)y = f(-x), we reflect the original graph of y=f(x)y = f(x) across the y-axis. This means that for every point (x,y)(x, y) on the original graph, the corresponding point on the new graph will be (−x,y)(-x, y). The key points to plot include:

  • (0,0)(0, 0)
  • (2,2)(2, 2)
  • (4,0)(4, 0)
  • (−2,2)(-2, 2)
  • (−4,0)(-4, 0)

Plot these points and connect them smoothly to complete the reflection.

Step 2

Find an equation for $S$

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Answer

The point (1,6)(1, 6) on curve CC transforms to (4,6)(4, 6) on curve SS. This indicates a horizontal translation of 3 units to the right.

The original equation is: y=5+2x−x2y = 5 + 2x - x^2

To find the equation of SS, we substitute x−3x - 3 for xx in the equation of curve CC:

y=5+2(x−3)−(x−3)2y = 5 + 2(x - 3) - (x - 3)^2

Expanding this, we have: y=5+2x−6−(x2−6x+9)y = 5 + 2x - 6 - (x^2 - 6x + 9) y=2x−1−x2+6x−9y = 2x - 1 - x^2 + 6x - 9

oy=−x2+8x−10y = -x^2 + 8x - 10 Therefore, the equation for curve SS is: y=−x2+8x−10y = -x^2 + 8x - 10

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