Find the equation of the parabola, with axis of symmetry of the y-axis, which passes through the points 𝐴(−2,1) and 𝐵(4, −5).

Answer 1

ax^2 + bx + c = y

(-2,1) --> 4a -2b + c = 1

(4,-5) --> 16a + 4b + c = -5

subtracting them: 12a + 6b = -6

2a + b = -1

-b/2a = 0 since axis of symmetry is the y-axis

b = 0

then a = -1/2

4a -2b + c = 1

-2 - 0 + C = 1

-2+c = 1

c=3

and

16a + 4b + c = -5

-8 + c = -5

c = 3

y = (-1/2)x^2 + 3