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?
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)
