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