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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Trying "intercept form",
y=a%28x-r%29%28x-s%29 for roots or zeros r and s,

a%28x%2B8%29%28x-1%29=0, according to the two given roots.

The other given point:
a%28x%2B8%29%28x-1%29=y
a%282%2B8%29%282-1%29=-20
a%2A10%2A1=-20
10a=-20
highlight%28a=-2%29

The equation for the three given points is therefore highlight%28y=-2%28x%2B8%29%28x-1%29%29.

You can decide for yourself if using the intercept method is better and discuss it. We only needed to handle two equations using the intercept form.

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
In this case  THE FASTEST METHOD  is  THIS: 

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 = -20%2F10 = -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.