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I know that the first term is a quadratic and I suppose that lets us know we are dealing with identifying a curve, and the third term is our constant. I just can't quite put it all together as how they are actually working together. Such as what relationship that have to each other.. Help.

amWhy
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Quintinium
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  • I'm speaking of equations like, x^2 + 2x +15. I'm wanting to understand what the question is really asking and what type of problems would require or could be answered with this type of equation. – Quintinium Mar 07 '14 at 19:47
  • Quadratics will be much easier to visualize if you convert them to $y = A(x - j)^2 + k$. Before that though you have to learn general theory like $f(x - j)$ is $f(x)$ shifted to the right by $j$. – DanielV Mar 08 '14 at 14:53
  • Just for reference: http://math.stackexchange.com/questions/647753/how-can-one-calculate-iiii/ – Caleb Stanford Mar 08 '14 at 16:00

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For the function $y=x^2 + bx + c$, where the lead coefficient is $1$, the second coefficient $b$, with its sign flipped, tells you the sum of the two $x$-intercepts, while the constant term $c$ tells you their product.

In the case of $x^2+2x+15$, you know that, if it has $x$-intercepts, then their sum is $-2$ and their product is $15$. There are no two real numbers satisfying those conditions, so this quadratic has no $x$-intercepts.

Does this address the question you're asking?

G Tony Jacobs
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