Write an equation for a quadratic function such that f(-5)=0 and f(9)=0
+118723 Write an equation for a quadratic function such that f(-5)=0 and f(9)=0
y=ax^2+bx+c
\(0=a*(-5)^2+b*-5+c \qquad (1)\\ 0=25a-5b+c \qquad (1b)\\ and\\ 0=a*(9)^2+b*9+c \qquad (2)\\ 0=81a+9b+c \qquad (2b)\\~\\ so\\ 25a-5b+c=81a+9b+c\\ 25a-5b=81a+9b\\ -14b=56a\\ b=-4a\\~\\ c=5b-25a=-20a-25a=-45a\\ c=-81a-9b=-81a+36a=-45a\\ Let\;a=1\\ then\;\;b=-4 \qquad and \qquad c=-45\\ \mbox{So a solution is}\\ y=x^2-4x-45 \)
+130516 Easy
f(x) = (x + 5) (x - 9) = x^2 -4x - 45
Here's the graph ..... https://www.desmos.com/calculator/o71jos4cwn
+118723 LOL
Nicely done Chris,
I knew there was an easy way !!
But you know, why fly across Mt Everest in air conditioned comfort when you could just climb over it. with ropes and oxygen tanks. 
All solutions can be expressed as That is assuming it is a concave up or down parabola with an axis of symmetry parallel to the y axis.
\(y=a ( x^2 -4x - 45) \qquad where \;\;a\in R\)
