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I was given the graph :

enter image description here

and was asked to say whether the coefficients $(a,b,c)$ of the function $ax^2+bx+c$ for each of the 2 graphs was either positive or negative. We are supposed to find these coefficients just looking at the graph. I figured that the a coefficient for $y=g(x)$ was negative and was positive for $y=f(x)$. I know that the c coefficient is negative for both, however I don't quite know what to say for the $b$ coefficient because I don't really understand the behaviour of the $b$ coefficient. We are also asked to find the discriminant for each graph: "In each case is $b^2 > 4ac$ or $b^2 < 4ac$?" But I'm not sure what $2$ roots or $1$ root looks like on a graph.

MattAllegro
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jn025
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2 Answers2

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Hints:

  1. Given that you know how to determine the sign of "$c$", to find "$b$", think of the slope of the function at $x=0$.

  2. Roots $=$ number of times the graph intersects the $X$ axis...

Macavity
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  • for the roots I noticed that the discriminant formula is normally b^2-4ac > 0 but in this case its b^2 > 4ac? How does this impact the number of roots? – jn025 May 19 '14 at 12:19
  • You need to brush up on discriminants (maybe check http://www.khanacademy.org/math/algebra2/polynomial_and_rational/quad_formula_tutorial/v/discriminant-of-quadratic-equations). First, note that both statements you wrote are equivalent. $b^2-4ac > 0 \iff b^2 > 4ac$. Further, if the discriminant - i.e. $b^2-4ac$ is positive, you have two real roots, if it is zero there is exactly one distinct root, and if the discriminant is negative, you have no real roots. – Macavity May 19 '14 at 12:59
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Hint:

The vertex lies at $x=-\frac{b}{2a}$.

poolpt
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