A parabola is shown below. Its vertex and another point on the parabola are labeled. Write an equation of the parabola. yx (1,3), (2,-1)

Answer 1

(1,3) and (2,-1)

if (1,3) is the vertex, then axis of symmetry is x=1 for a standard downward opening parabola of the form y= a(x-h)^2 + k where (h,k) is the vertex and y=a(x-1)^2 +3. to find "a" plug in the other point (2,-1) -1 = a +3, a =-4

the parabola is y =-4(x-1)^2 + 3

if (2,-1) is the vertex, then y=a(x-2)^2 -1 and 3=a(1-2)^2 -1

a = 3+1 =4

y = 4(x-2)^2 -1

that assumes a vertically opening parabola. You could also find left and right opening parabolas, as well as an infinite number of other parabolas at angles other than 0 and 90 degrees