15 (a) Write $x^2 - 8x + 25$ in the form $(x - a)^2 + b$ - OCR - GCSE Maths - Question 15 - 2018 - Paper 1
Question 15
15 (a) Write $x^2 - 8x + 25$ in the form $(x - a)^2 + b$.
(b) Write down the coordinates of the turning point of the graph of $y = x^2 - 8x + 25$.
(c) Hence des... show full transcript
Worked Solution & Example Answer:15 (a) Write $x^2 - 8x + 25$ in the form $(x - a)^2 + b$ - OCR - GCSE Maths - Question 15 - 2018 - Paper 1
Step 1
Write $x^2 - 8x + 25$ in the form $(x - a)^2 + b$.
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Answer
To write the expression in the form (x−a)2+b, we complete the square.
Start with the quadratic expression: x2−8x+25
Take half of the coefficient of x, which is −8: rac{-8}{2} = -4
Square this value: (−4)2=16
Rewrite the expression by adding and subtracting this square: x2−8x+16+25−16
This simplifies to: (x−4)2+9
Thus, the expression is written as: (x−4)2+9.
Step 2
Write down the coordinates of the turning point of the graph of $y = x^2 - 8x + 25$.
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Answer
From the completed square form of the quadratic, y=(x−4)2+9, we can identify the turning point. The vertex of the parabola is at (4,9).
Thus, the coordinates of the turning point are: (4,9).
Step 3
Hence describe the single transformation which maps the graph of $y = x^2$ onto the graph of $y = x^2 - 8x + 25$.
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Answer
To describe the transformation, observe that the graph of y=x2 has been translated. Since we found the turning point to be at (4,9), this indicates a translation.
The graph is moved right by 4 units and up by 9 units.
Thus, the transformation can be described as:
[ ext{Translation } \left( 4, 9 \right) \text{ (right 4 and up 9)} \right] ]
