1. ## Find Parabola Equation

What is the equation of a parabola that goes through points (0,1), (–1,6), and (2,3)?

2. Hello

Originally Posted by magentarita
What is the equation of a parabola that goes through points (0,1), (–1,6), and (2,3)?
a parabola has the form f(x) = ax^2 + bx + c

f(0) = a*0 + 0*b + c = 1

f(-1) = a*(-1)^2 + b*(-1) + c = 6

f(2) = a*(2)^2 + b*(2) + c = 3

Can you solve these three equations? yes YOU can

[solution: c = 1, a=2, b=-3]

=> f(x) = 2x^2-3x+1 is the equation of the parabola that goes through the given points (0,1), (–1,6), and (2,3)

Regards,
Rapha

3. ## ok...............

Originally Posted by Rapha
Hello

a parabola has the form f(x) = ax^2 + bx + c

f(0) = a*0 + 0*b + c = 1

f(-1) = a*(-1)^2 + b*(-1) + c = 6

f(2) = a*(2)^2 + b*(2) + c = 3

Can you solve these three equations? yes YOU can

[solution: c = 1, a=2, b=-3]

=> f(x) = 2x^2-3x+1 is the equation of the parabola that goes through the given points (0,1), (–1,6), and (2,3)

Regards,
Rapha
It's easier than I thought.

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### find the equation of the parabola that passes through (6,1)

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