Question

What's the equation

Answer 1

Given:

The graph of a parabola.

To find:

The equation for the parabola.

Solution:

The vertex form of a parabola is:

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

Where, a is a constant and (h,k) is the vertex.

From the given graph it is clear that the vertex of the parabola is at point (-1,6). So, h=-1 and k=6.

Putting h=-1 and k=6 in (i), we get

`y=a(x-(-1))^2+(6)`

`y=a(x+1)^2+6` ...(ii)

The y-intercept of the graph is at point (0,3). Putting x=0 and y=3 in (ii), we get

`3=a(0+1)^2+6`

`3-6=a`

`-3=a`

Putting a=-3 in (ii), we get

`y=-3(x+1)^2+6`

Therefore, the equation of the parabola is
`y=-3(x+1)^2+6`.