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The parabola  is graphed below. Find abc. (The grid lines are one unit apart.)

 

https://latex.artofproblemsolving.com/3/d/c/3dcbfd37344accf75039423aaee0e135a89dc16a.png

Many people have said the answer is 30, but it has to be a fraction. Can someone PLEASE give me the correct answer?

 Mar 17, 2020
 #1
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What's the question?

 Mar 17, 2020
 #2
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Ok I'm gonna assume some things about this question because you didn't fully explain. I'm answering based on the assumption that you have to find a*b*c in the equation ax^2+bx+c = 0. Let's take a look at this parabola first. Realize that the equation is 

 

1/2 * x^2. Look at how "fast" the graph increases. At an x value of 2, the y value is 2. At an x value of 4, the value is 8. Compare that to a normal graph (y = x^2) in which an x value of 2 produces a y value of 4, and an x value of 4 produces 16, and it's clear that the parabola has a coefficient of 1/2 in front of the x^2 term. With that being said, the problem becomes quite simple. We know the vertex of the parabola which is -3, -2. With that in mind, we can rewrite the parabola into vertex form, which is

 

a(x -h)^2 + k   with the vertex being (h,k), and a being the coefficient

 

This gives us 1/2(x+3)^2 - 2, which simplifies to 1/2x^2 + 3x + 5/2. Since the question(presumably) asks us for a * b * c, we get 1/2 * 3 * 5/2, which gives us an answer of 15/4.(Please correct me if I'm wrong)

 Mar 18, 2020

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