Write an equation any form for the quadratic graphed below y

Write an equation (any form) for the quadratic graphed below y = _____________

Solution

the vertex of the graph is -1 , -4

standard equation in vertex form is given by

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

where h , k is the vertex

plugging the values of the vertex

y = a ( x + 1)^2 - 4

finding the value of a from y intercept

y intercept is -2

-2 = a ( 0+1)^2 - 4

-2 + 4 = a

a = 2

hence, equation of the function is

y = 2 ( x+1)^2 - 4