or A parabola opening up or down has vertex (0,1) and passes through (4,5). Write its equation in vertex form.

Question

Simplify any fractions.

Answer 1

vertex (0,1) and the parabola passing through (4,5) means an upward opening parabola

vertex = the minimum point. axis of symmetry is x=0

if (4,5) is on the graph then so is a symmetrical point (-4,5)

y=a(x-0)^2 + 1

y =ax^2 +1

plug in (4,5) to solve for a

5=16a +1

a =1/4

the parabola equation is:

y = (1/4)x^2 +1 in vertex form

vertex form is y=a(x-h)^2 + k where (h,k) is the vertex =(0,1) h=0, k=1