Find the vertex of the parabola with focus at (0,7) and passes through the points (±2, 7) and (±1, 5).

Question

It would be nice if the solution is also stated so I can understand it more thoroughly. Thank you!

Answer 1

(0,7) focus

(2,7), (-2,7), (1,5) and (-1,5) are points on a parabola

try plotting all five points

an upward opening parabola has a general form of

y =a(x-h)^2 +k with vertex (h,k) = (0,k) and a>0, axis of symmethry is the y axis

7 = a(2)^2 + k

7= 4a+k

5 =a+k

7=4(5-k)+k

3k=13

k=13/3

vertex is (0, 4 1/3)

y= (2/3)x^2 +13/3

or

3y = 2x^2 + 13