# algebra

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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 -

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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