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Given that f(x) = x^2 - 4x + 5 x ∈ ℝ a) express f(x) in the form (x + a)^2 + b where a and b are integers to be found - Edexcel - A-Level Maths Pure - Question 4 - 2021 - Paper 1
Question 4
Given that f(x) = x^2 - 4x + 5 x ∈ ℝ a) express f(x) in the form (x + a)^2 + b where a and b are integers to be found. The curve with equation y = f(x) • meets ... show full transcript
Worked Solution & Example Answer:Given that f(x) = x^2 - 4x + 5 x ∈ ℝ a) express f(x) in the form (x + a)^2 + b where a and b are integers to be found - Edexcel - A-Level Maths Pure - Question 4 - 2021 - Paper 1
Step 1
a) express f(x) in the form (x + a)^2 + b where a and b are integers to be found.
Answer
To express the function in the desired form, we will complete the square:
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Start with the original function:
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Take the coefficient of x, which is -4, halve it to get -2, and square it to find 4.
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Rewrite the function by adding and subtracting this square:
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This simplifies to:
Thus, we find that a = -2 and b = 1.
Step 2
Step 3
b) Write down (ii) the coordinates of Q.
Answer
To find the coordinates of Q, we need the x-coordinate of the minimum turning point. Since this is at the vertex of the parabola, for the expression (x - 2)^2 + 1, the vertex occurs at x = 2. Substituting x = 2 into f(x):
Thus, the coordinates of Q are (2, 1).