algebra
posted by Sandra .
A parabola has xintercepts at 3 and 7, a yintercept at 21, and (5,4) for its vertex. Write the parabola’s equation

Sketch those points on a graph.
It is an upside down parabola (sheds water)
The axis of symmetry is x = 5
when x = 5, y = 4
so
for starters
y4 = c (x5)^2
That is the same both sides of x = 5
and y = 4 when x = 5
We need c
put in one of those other points
for example (0,21)
21 4 = c (5)^2
25 = c (25)
c = 1
so
y4 = (x5)^2
or
y = 4  (x5)^2
check with (3,0)
? = 4 (2)^2
? = 4  4
0 sure enough