C1 question on graph please help !!

The question is to sketch the graph of y=x^2+12x+1 but i dont know how because the previous question asks to complete the square which is y=(x+6)^2 -35
then the second part of the question asks to solve the equation which I got -6+-root 35. The answer is (6,35) (0,1) and (-6+-root 35,0) can anyone explain? Thanks

I'll explain the best I can.

When you complete th square you find it's vertex(minimum point) in this case it is (-6,-35) so first plot that.

It intercepts y at +1 so next plot that.

Find the x intercepts as you have done so -6+root 5 will be plotted as a rough estimate at around x is - 3.5 and then -6-root 5 will be plotted roughly at - 8.5 and then dear the curve.

why would it intercepts y at 1? so the completing the square bit is to work out the minimum point, i get that. But is there a turning point though as from the completing the square bit i got (x+6) (x+6)-35 so wouldn't x be -6 and i don't get what the -6+root 35 part is for. Thanks

why would it intercepts y at 1? so the completing the square bit is to work out the minimum point, i get that. But is there a turning point though as from the completing the square bit i got (x+6) (x+6)-35 so wouldn't x be -6 and i don't get what the -6+root 35 part is for. Thanks

When you got your original equation you got the original ax^2 + bx + c format to find the y intercept let x be equal to zero therefore you will have y = 0+0+1 therefore the line intercepts the y axis at 1.

When drawing a quadratic graph you only ever have one minimum or maximum point - you can never have 2. This is why completing the square is used as it shows the minimum values possible in this case you got it to equal (x+6)^2 -35. When drawing the vertex/Turning point forget the bracket is squared and look inside the bracket you want x + 6 to equal zero so the minimum x can be is - 6. To get the y value you look at the -35 as the bracket is equal to 36 and you just want the value of 1 so the minimum y can be is -35. So the vertex/turning point is (-6,-35).

For the root bit your confused on it corresponds to the x intercept. When you root an answer you get a negative and a positive (in a lot of cases) so you treat them differently and plot them on the graph they don't have to be too accurate so just label them. Remember the values of your x as negative so there will go in the bottom left quadrant of the graph

In the original equation if x=0 then y= 1 thats why it intercepts at y=1.

When you solved it you worked out where it crossed the x axis so when you sketch it you just roughly plot the -6 + sqrt35 and -6 - sqrt35 they should both be minus number when your curve comes upwards it goes through x=1 after passing over the x axis. Google graph drawer and have it drawn and im sure you will understand