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Find the coordinates of the turning point of the graph of $y = x^2 + 6x + 17.$ - OCR - GCSE Maths - Question 14 - 2021 - Paper 1
Question 14
Find the coordinates of the turning point of the graph of $y = x^2 + 6x + 17.$
Worked Solution & Example Answer:Find the coordinates of the turning point of the graph of $y = x^2 + 6x + 17.$ - OCR - GCSE Maths - Question 14 - 2021 - Paper 1
Step 1
Step 2
Step 2: Complete the square
Answer
To find the turning point, we can complete the square. Starting with the equation:
We focus on the quadratic and linear parts:
Next, to complete the square for , we take half of 6, which is 3, square it to get 9, and rewrite the equation:
Thus, the equation simplifies to:
Step 3
Step 3: Identify the turning point
Answer
From the completed square form, , we can identify the turning point. The vertex of the parabola occurs at the point where the squared term is equal to zero. Therefore, the -coordinate of the turning point is and the -coordinate is
Thus, the coordinates of the turning point are