I'm working through the Pearson Edexcel Pure Mathematics Year 1/ AS practice book. I've been over this question twice using different methods, and I really think they've made a mistake. I'd be grateful for anyone else who can cast their eye over my working and see if it's me or them who's mistaken...
The question is "Find the coordinates of the turning point of y = -x^2 - 13x - 42".
Here's one of the methods I used to find the turning point:
y = -x^2 - 13x - 42 --> Multiply everything by -1
y = x^2 + 13x + 42 --> Complete the square
y = (x + 13/2)^2 - 169/4 + 42 --> Put everything outside the bracket /4
y = (x + 13/2)^2 - 169/4 + 168/4 --> Simplify
y = (x + 13/2)^2 - 1/4
--> Turning point is (-13/2, -1/4)
The other method I tried was just to factorise out -1 at the start and put everything else in square brackets, then complete the square as normal.
Both methods returned me coordinates of (-13/2, -1/4).
However the book says the answer should be (-13/2, 1/4).
It doesn't show how they arrived at that answer.
Am I mistaken, or are they?!