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 10 - 2013 - Paper 1
Question 10
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)... 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 10 - 2013 - Paper 1
Step 1
Sketch the curve C with equation y = f(x + 2)
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Answer
To sketch the curve C, we will apply a horizontal translation of the original function f(x). The transformation changes the input x to (x + 2), shifting the graph 2 units to the left. The x-intercepts will be adjusted as follows:
The point (1, 0) shifts to (-1, 0).
The point (-3, 0) shifts to (-5, 0).
Based on this, the x-intercepts for the new function are now at (-1, 0) and (-5, 0). The y-intercept can be found by substituting x = 0 into the equation for the curve C. We will find that the curve C meets the x-axis at the coordinates (-1, 0) and (-5, 0).
Step 2
Write down an equation of the curve C.
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Answer
The equation for the curve C can be expressed as:
(x+5)(x+1)(x−1)
Here, we have factored the equation taking into account that the x-intercepts have changed due to the horizontal shift.
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 coordinates of where the curve C meets the y-axis, we substitute x = 0 into the equation from part (b):
