We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

A parabola $ax^2+bx+c$ contains the points $(-1,0)$, $(0,5)$, and $(5,0)$. Find the value $100a+10b+c$.

 Nov 10, 2019

Plug in the x values in the coordinates into the parabola equation. then set it equal to the y-value in the coordinates.


So we get 3 equations





Simplifies to:




Plugging C we get two equations




We simplify:




We simplify further:




We use elimination (addition):




Plugging back a = -1 into \(a-b=-5\)


We get \(b=4\)


So we have \((a,b,c)=(-1,4,5)\)



I will leave evaluating \(100a+10b+c\) up to you now.

Can you solve the problem?

 Nov 10, 2019

8 Online Users