Question

What is the equation of the parabola that has its vertex at (7,6) and contains the point (6,8)?

Answer 1

Explanation:

y = 2x2 – 28x + 52

wrong its not that

Answer 2

`y = 2 (x-7)^(2) +6` is the equation of parabola.

Explanation:

Vertex form of a parabola is given as :

`y = a (x-h)^(2) +k ...... (1)`

(h,k) is the co-ordinate of vertex of parabola.

(x,y) are the points on parabola.

We are given that vertex is at (7,6) and a point on parabola is (6,8).

h = 7

k = 6

x = 6 and

y =8

Putting all the values in equation (1):

`8 = a (6-7)^(2) +6\\\Rightarrow 8 = a + 6\\\Rightarrow a = 2`

Putting values of (h,k) and a in equation (1) to obtain the equation of parabola:

`y = 2 (x-7)^(2) +6` is the equation of parabola with vertex at (7,6) and contains the point (6,8).