SOLUTION: you use a system with three variables to find the equation of a parabola that passes through the points (-8,0) (2,-20) and (1,0). Your friend uses intercept form to find the equati
Question 1100471: you use a system with three variables to find the equation of a parabola that passes through the points (-8,0) (2,-20) and (1,0). Your friend uses intercept form to find the equation. whose method is easier? justify your answer. Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39617) (Show Source):
This parabola (quadratic polynomial) has the roots x= -8 and x= 1 (where y is equal to zero).
Hence, the quadratic polynomial has the form p(x) = a*(x-(-8))*(x-1) = a(x+8)*(x-1) with the unknown coefficient "a".
To determine the value of "a", use the condition/(the fact from the condition) that
p(2) = -20 = a(2+8)*(2-1) = a*10*1 = 10*a.
It gives you a = = -2.
and finally your polynomial has the form
p(x) = -2*(x+8)*(x-1).
You can transform it further to any form you wish.
Under this approach, you do not need solve any systems of equations.
If your friend uses this method, he is on the right track.