Photo AI

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

Question icon

Question 22

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

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 cur... show full transcript

Worked Solution & Example Answer: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

Sketch the graph of the curve with equation $y = f(-x)$

96%

114 rated

Answer

To sketch the graph of y=f(−x)y = f(-x), we reflect the original graph across the y-axis. Each point (x,f(x))(x, f(x)) on the original curve will now correspond to the point (−x,f(x))(-x, f(x)) on the new graph. This will lead to a symmetric graph with respect to the y-axis.

Step 2

Find an equation for $S$

99%

104 rated

Answer

To find the equation of curve SS, we first identify the translation that moves the point (1,6)(1, 6) on curve CC to the point (4,6)(4, 6) on curve SS. The translation involves a shift of 3 units to the right. Thus, the new equation SS can be represented as:

y=f(x−3)y = f(x - 3)

Substituting the original function into this translation: y=5+2((x−3))−(x−3)2y = 5 + 2((x - 3)) - (x - 3)^{2} This simplifies to: y=5+2x−6−(x2−6x+9)y = 5 + 2x - 6 - (x^{2} - 6x + 9) y=−x2+8x−10y = -x^{2} + 8x - 10 Thus, the equation for SS is: y=−x2+8x−10y = -x^{2} + 8x - 10

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;