SOLUTION: A parabola passes through (2,0), (3,0) and (0,3). Find it's equation.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A parabola passes through (2,0), (3,0) and (0,3). Find it's equation.      Log On


   

Question 356349: A parabola passes through (2,0), (3,0) and (0,3). Find it's equation.
Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since it has zeros at x=2 and x=3, the quadratic equation has the form,
f%28x%29=a%28x-2%29%28x-3%29
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Use the last point (0,3) to find a.
f%280%29=a%280-2%29%280-3%29=3
a%286%29=3
a=1%2F2
f%28x%29=%281%2F2%29%28x-2%29%28x-3%29
f%28x%29=%281%2F2%29%28x%5E2-3x-2x%2B6%29
f%28x%29=%281%2F2%29%28x%5E2-5x%2B6%29
highlight%28f%28x%29=%281%2F2%29x%5E2-%285%2F2%29x%2B3%29
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Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

parabola passes through(2,0), (3,0) and (0,3). 



PT(2,0)and PT(3,0) tells us the axis of symmetry is x = 2.5 and 2.5 is the x value of the vertex



y = a(x-2)(x-3)

3 = a*6

1/2 = a

y=+a%28x-h%29%5E2+%2Bk   (h,k) is the vertex

y+=+%281%2F2+%29%28x+-+2.5%29%5E2+%2B+b

(3,0)

0 = 1/2 * 1/4 + b

b = -1/8

y = .5(x-2.5) -1/8