Question

A parabola opening up or down has a vertex (0,4) and passed through (-4,2) write its equation in vertex form

Answer 1

f(x) = -2x^2 + 4

or

f(x) = -2(x+0)^2 + 4

Explanation:

Vertex form is written as

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

where h and k are (x,y) of the vertex

Start by plugging these two values into the equation

f(x) = a (x- (0) )^2 + 4

Simplify

f(x) = ax^2 + 4

Next plug in the values of the second point for ( f(x),y )

-4 = a(2)^2 + 4

Solve

-4= 4a +4

-8=4a

-2=a

Plug -2 in for a in the initial equation

f(x) = -2x^2 + 4