Find the coordinates of the turning point of the graph of $y = x^2 + 6x + 17.$ - OCR - GCSE Maths - Question 14 - 2021 - Paper 1

To find the turning point, we can complete the square. Starting with the equation:

$y = x^2 + 6x + 17$

We focus on the quadratic and linear parts:

$y = (x^2 + 6x) + 17$

Next, to complete the square for $x^2 + 6x$, we take half of 6, which is 3, square it to get 9, and rewrite the equation:

$y = (x + 3)^2 - 9 + 17$

Thus, the equation simplifies to:

$y = (x + 3)^2 + 8$

From the completed square form, $y = (x + 3)^2 + 8$, 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 $x$-coordinate of the turning point is $-3$ and the $y$-coordinate is $8.$

Thus, the coordinates of the turning point are $(-3, 8).$