SOLUTION: 1)Find the equation of the parabloa with points (5,0) and (6,10). 2)Find the equation of the parabola with points (1,5) and (2,10). *Please explain step by step. Thank you.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 1)Find the equation of the parabloa with points (5,0) and (6,10). 2)Find the equation of the parabola with points (1,5) and (2,10). *Please explain step by step. Thank you.      Log On


   

Question 442622: 1)Find the equation of the parabloa with points (5,0) and (6,10).
2)Find the equation of the parabola with points (1,5) and (2,10).
*Please explain step by step.
Thank you.
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Since we know that it passes through the point (5,0), then (x-5) is a linear factor.
x-5 | ax^2 + bx +5
So, dx-1 must be the other factor.
Since 10 = (6-5)(6d-1), then 10 = 1(6d-1) , so d = expr%2811%2F6%29
(x-5)((11/6)x-1) = 4/3x^2 - 20/3x +2x -10
expr%2811%2F6%29x%5E2+-+55%2F6x+-x+%2B5+=++expr%2811%2F6%29x%5E2+-+expr%2861%2F6%29x+%2B5
So our answer is expr%2811%2F6%29x%5E2+-+expr%2861%2F6%29x+%2B+5+
For the second one:
a(1^2) + b(1) + c = 5
a(2^2) + b(2) + c = 10
---------------------
Since 4a + 2b +c = 10
and a + b + c = 5

3a + b + 0c = 5
0a -2b -3c = -10
2a +0b -2c = -15
add equations 1 and 3 together to get
5a + b -2c = -10
Notice 2b + 3c = 10
Then 5a + 3b + c = 0
Recognize that a+b+c = 5 and 3a+b = 5
Then a+b+c = 3a +b. Meaning 2a =c.
Then 2a -2c = -15
c - 2c = -15 -c = -15 so c =15.
Remember that 2b + 3c = 10
2b + 45 = 10
2b = -35
b = -35/2
Remember 3a + b = 5.
3a -35/2 = 5
6a - 35 = 10
6a = 45
a = 45/6 or 15/2
So our parabola is expr%2815%2F2%29x%5E2+-expr%2835%2F2%29x+%2B+15
Wow that was a toughy!
Hope this helped!