C1 curve intersection question please help

Would you please help me to see whether i'm tackling this problem in the right way?


It says: Find the coordinates of the points of intersection of the curve y=(x-4)^2-3 with the x-axis and the y-axis, using surds when necessary. [4]


So I made x = 0 and then said:
y=(-4)^2 - 3
y=16-3
y=13
=> the coordinates of the point of intersection of the curve with the y axis are (0,13)


then I made y=0 and formed a quadratic to find X
x^2 -8x + 13 = 0


I ended up with 4 +/- 2sqrt3


so I said coordinates of intersection with the xaxis = (4 + 2 sqrt3, 0)
or x = (4 - 2sqrt3, 0)


would this get me all 4 marks?

Would you please help me to see whether i'm tackling this problem in the right way?


It says: Find the coordinates of the points of intersection of the curve y=(x-4)^2-3 with the x-axis and the y-axis, using surds when necessary. [4]


So I made x = 0 and then said:
y=(-4)^2 - 3
y=16-3
y=13
=> the coordinates of the point of intersection of the curve with the y axis are (0,13)


then I made y=0 and formed a quadratic to find X
x^2 -8x + 13 = 0


I ended up with 4 +/- 2sqrt3


so I said coordinates of intersection with the xaxis = (4 + 2 sqrt3, 0)
or x = (4 - 2sqrt3, 0)


would this get me all 4 marks?

Would you please help me to see whether i'm tackling this problem in the right way?

I ended up with 4 +/- 2sqrt3