Figure 1 shows a sketch of the curve with equation y = f(x) where
f(x) = (x + 3)² (x - 1),
x ∈ ℝ - Edexcel - A-Level Maths Pure - Question 9 - 2013 - Paper 1
Question 9
Figure 1 shows a sketch of the curve with equation y = f(x) where
f(x) = (x + 3)² (x - 1),
x ∈ ℝ.
The curve crosses the x-axis at (1, 0), touches it at (-3, 0) a... show full transcript
Worked Solution & Example Answer:Figure 1 shows a sketch of the curve with equation y = f(x) where
f(x) = (x + 3)² (x - 1),
x ∈ ℝ - Edexcel - A-Level Maths Pure - Question 9 - 2013 - Paper 1
Step 1
Sketch the curve C with equation y = f(x + 2) and state the coordinates of the points where the curve C meets the x-axis.
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Answer
To find the equation of the curve C, we need to apply a horizontal translation to the original function f(x). This means replacing x with (x + 2):
f(x+2)=((x+2)+3)2((x+2)−1)=(x+5)2(x+1)
The original x-intercepts were at (1, 0) and (-3, 0). To find the new x-intercepts, we solve (x+5)2(x+1)=0
This gives us: x = -5 (double root) and x = -1. Therefore, the x-intercepts are at (-5, 0) and (-1, 0).
The sketch will show a cubic curve that crosses the x-axis at (-5, 0) and (-1, 0). It should touch the x-axis at x = -5 and cross at x = -1.
Step 2
Write down an equation of the curve C.
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Answer
The equation of the curve C is:
y=(x+5)2(x+1)
Step 3
Use your answer to part (b) to find the coordinates of the point where the curve C meets the y-axis.
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Answer
To find the y-intercept, we substitute x = 0 into the equation of the curve:
y=(0+5)2(0+1)=25(1)=25
Thus, the coordinates of the point where the curve C meets the y-axis are (0, 25).
