SOLUTION: Could someone explain too me, how to solve this problem, it would be much appreicated. A parabola with equation y = ax^2 + bx passes through the two points (-1,3) and (4,-2). (

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Could someone explain too me, how to solve this problem, it would be much appreicated. A parabola with equation y = ax^2 + bx passes through the two points (-1,3) and (4,-2). (      Log On


   

Question 642119: Could someone explain too me, how to solve this problem, it would be much appreicated.
A parabola with equation y = ax^2 + bx passes through the two points (-1,3) and (4,-2).
(a) Use algebra to find its equation.
Hint: Set up a system of two simultaneous equations.
and could you please explain the steps you go through to get the end result.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A parabola with equation y+=+ax%5E2+%2B+bx passes through the two points (-1,3) and (4,-2)
you need to find the three unknown coefficients a and b
Insert each of the 2 points and you will get 2 equations with 2 unknowns:
3+=+a%28-1%29%5E2+%2B+b%28-1%29.....1
-2+=+a%284%29%5E2+%2B+b%284%29.....2
_____________________solve this system by substitution
3+=+a%28-1%29%5E2+%2B+b%28-1%29.....1....solve for a
3+=+a+-b
3+%2Bb=+a ..........................substitute in 2
-2+=+%283+%2Bb%29%284%29%5E2+%2B+b%284%29.....2....solve for b
-2+=+%283+%2Bb%29%2A16+%2B+4b
-2+=+48+%2B16b+%2B+4b
-2+-+48+=20b
-50=20b
highlight%28-2.5=b%29
now find a
3+%2Bb=+a
3+-2.5=+a
highlight%280.5=+a%29
y+=+ax%5E2+%2B+bx........plug in a and b
y+=0.5x%5E2+-2.5x

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+0.5x%5E2+-2.5x%29+