Question

What is the equation of a parabola y(x) that has a vertex at point (− 1/3 , 0.3) and passes through point (− 2/15 , − 1/2 ).

Answer 1

`y=-20(x+(1)/(3))^2+0.3`

Explanation:

The vertex form of a parabola is given by

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

Here (h,k) is the vertex.

We have been given that vertex is at (− 1/3 , 0.3) . Thus, the vertex form of the parabola is

`y=a(x+(1)/(3))^2+0.3`

Now, it passes through point (− 2/15 , − 1/2 ). Thus, we have

`-(1)/(2)=a(-(2)/(15)+(1)/(3))^2+0.3\\\\(1)/(25)a+0.3=-(1)/(2)\\\\(1)/(25)a+0.3-0.3=-(1)/(2)-0.3\\\\(1)/(25)a=-0.8\\\\a=-20`

Therefore, equation of parabola is given by

`y=-20(x+(1)/(3))^2+0.3`