SOLUTION: can you give me a detailed way of how to solve a Parabola through 3 given points? the points are (0,2),(3,0),and (5,2). thx.

Question 2075: can you give me a detailed way of how to solve a Parabola through 3 given points? the points are (0,2),(3,0),and (5,2). thx.
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
Assume the quadratic function (parabloa) is
y = ax^2 +bx + c,
Solve: 2 = 0+0+c =c...(1)
0 = 9a + 3b + c ...(2)
2 = 25a + 5b + c...(3)
Replace c by 2,(2),(3) become
9a + 3b + 2 =0 ...(2)
5a + b = 0...(3)
From (3): b =-5a, and goto (2), we have:
9a - 15a+ 2 =0, or -6a = -2, a = 1/3.
So, b = -5/3.
Hence, the function is y = x^2/3 - 5x/3 + 2
Also,if you notice that the parabola passing (0,2) & (5,2)(same y value)
Let y = k(x - 0)(x-5) + 2,
Set x =3, we have 0 = k*3*(-2) + 2, so k = 1/3.
Thus,we obtain the same answer y = x(x-5)/3 + 2 = x^2/3 - 5x/3 + 2

Kenny

RELATED QUESTIONS
I have struggled with this equation, and I still cannot get the answer to come out... (answered by ewatrrr)

Can you give me a detailed explanation of how to solve 3-8x=1... (answered by Fombitz,jessica43)

Find the equation of a parabola through each set of three points. You do NOT have to... (answered by Alan3354)

I solved the quadratic equation of 3x^2+11x-20=0 by factoring and have the correct answer (answered by Fombitz)

Write the equation of the line passing through each of the given points with the... (answered by Nate)

Choose the true statement of y is less than or equal to 5x^2 + 6x + 2 Points on the... (answered by Fombitz)

How to write an equation of a line with the given slope and y-intercept? 1. m= 3/7... (answered by chitra)

Hi how do you find the equation of a parabola given 3 points: (-1,-2), (1,-4) and... (answered by josgarithmetic)

The graph of a parabola passes through the points (3/2, 4/3) and (0, −6) and has a... (answered by ikleyn)