if the point (3, 9) is on the parabola y = x², what would the coordinates of this point become: a) if the…

if the point (3, 9) is on the parabola y = x², what would the coordinates of this point become: a) if the parabola was shifted up three units and left 2 units? b) if the parabola was shifted down 1 unit and right 5 units? the answer is: a) (1,12) b) (8,8) is your answer correct?

if the point (3, 9) is on the parabola y = x², what would the coordinates of this point become: a) if the parabola was shifted up three units and left 2 units? b) if the parabola was shifted down 1 unit and right 5 units? the answer is: a) (1,12) b) (8,8) is your answer correct?

Answer

Explanation:

Step1: Recall transformation rules

For a parabola (y = x^{2}), a shift up (k) units and left (h) units gives the new - function (y=(x + h)^{2}+k), and a shift down (k) units and right (h) units gives (y=(x - h)^{2}-k). For a point ((x,y)) on the original parabola, the transformation of the point follows the opposite rules.

Step2: Solve part a

The parabola is shifted up 3 units and left 2 units. For a point ((x,y)=(3,9)) on the original parabola, the new (x) - coordinate is (x'=3-2 = 1) (opposite of left - shift for the point) and the new (y) - coordinate is (y'=9 + 3=12) (same as up - shift for the point).

Step3: Solve part b

The parabola is shifted down 1 unit and right 5 units. For the point ((x,y)=(3,9)), the new (x) - coordinate is (x'=3 + 5=8) (opposite of right - shift for the point) and the new (y) - coordinate is (y'=9-1 = 8) (opposite of down - shift for the point).

Answer:

a) ((1,12)) b) ((8,8))