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

 Jul 14, 2022
 #1
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Using lagrange interpolation, the parabola is y = -5/2*x + 5/2*x 5, so 100a + 10b + c = 100(-5/2) + 10(5/2) + 5 = -220.

 Jul 14, 2022
 #2
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Because we are given both the roots of the quadratic, we can narrow the equation down to \(y = a(x+1)(x-5)\)

 

Now, think about how we can use the remaining coordinate (0,5) to solve for a...

 

Now that you know the quadratic, I assume you can take it from here

 Jul 15, 2022
edited by BuilderBoi  Jul 15, 2022

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