Posted by **Sandra** on Sunday, July 19, 2009 at 3:19pm.

A parabola has x-intercepts at 3 and 7, a y-intercept at -21, and (5,4) for its vertex. Write the parabola’s equation

- algebra -
**Damon**, Sunday, July 19, 2009 at 3:38pm
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

y-4 = c (x-5)^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

y-4 = -(x-5)^2

or

y = 4 - (x-5)^2

check with (3,0)

? = 4 -(-2)^2

? = 4 - 4

0 sure enough

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