How can you tell an equation's real or imaginary roots just from its graph, without knowing the equation? I have to look ath the graph of a parabola, absolute value, and a negative third degree equation and do so? Are there any links that could explain this as I can't scan in the problems to show you? Or could you just make a generalization?

You can make a generalization, but it involves Riemann surfaces, and you are not ready for that.

Look at this, and you will get an inkling. Everywhere a graph crosses the x axis is a real root, however, everwhere there is a minimum as in this graph, you can do this trick to pull out a pair of complex roots.
http://www.math.hmc.edu/funfacts/ffiles/10005.1.shtml

When looking at the graph of an equation, you can make some general observations to determine whether it has real or imaginary roots. Here are some guidelines for different types of equations:

1. Parabola: The graph of a parabola can have either two real roots, one real root (if it's a perfect square trinomial), or no real roots (if it does not intersect the x-axis). If the vertex of the parabola is above the x-axis, it has no real roots (i.e., only imaginary roots). If the vertex lies on the x-axis, the parabola has one real root. If the vertex is below the x-axis, the parabola has two real roots.

2. Absolute Value: The graph of an absolute value equation can intersect the x-axis at one point, indicating one real root, or it can touch the x-axis and bounce back up, indicating no real roots. If the absolute value equation intersects the x-axis in two distinct points, it has two real roots.

3. Negative Third Degree Equation: A negative third degree equation can have either one real root or three real roots. If the graph crosses the x-axis at one point, it has one real root. If the graph intersects the x-axis at three distinct points, it has three real roots. It's important to note that the exact number of roots cannot be determined solely from the graph, as there may be complex/imaginary roots.

Unfortunately, I cannot provide specific links as I am not able to browse the internet. However, you can search for topics like "graphing parabolas," "graphing absolute value equations," or "roots of polynomial equations" to find helpful resources and tutorials that explain these concepts visually.

Remember, these guidelines are generalizations, and for a more accurate analysis, it's always better to determine the equation mathematically.

To determine whether an equation has real or imaginary roots by looking at its graph, you need to consider the characteristics of each type of equation. While I cannot directly view the graphs you mentioned, I can provide a general explanation for each type of equation.

1. Parabola (quadratic equation):
A parabola is a U-shaped curve. If the parabola intersects the x-axis in two distinct points, then it has two real roots. This means that the equation has two solutions. If the parabola does not intersect the x-axis or is tangent to it, then it has no real roots, indicating that the equation has no solutions. In this case, the roots would be complex or imaginary.

2. Absolute value equation:
The graph of an absolute value equation often appears as a V-shaped curve. These equations generally have two solutions, unless the V-shaped curve is entirely above or entirely below the x-axis. If the V-shaped curve crosses the x-axis at two distinct points, then the equation has two real roots. If the curve does not intersect the x-axis or is tangent to it, then it has no real roots.

3. Negative third-degree equation:
A negative third-degree equation typically refers to a cubic equation with a negative leading coefficient. The graph of such an equation may involve multiple behaviors, including both real and imaginary roots. A generalization for determining real or imaginary roots from the graph alone would be complicated, as cubic equations can have various shapes. Analysing the exact behavior of the cubic equation graph would require considering additional factors like the curvature at different points.

While I cannot provide you with specific links without knowing the equations you have, you can search for resources on graphing different types of equations such as parabolas, absolute value equations, and cubic equations. Websites, video tutorials, and textbooks on algebra or calculus topics can provide detailed explanations with visual examples on how to recognize real or imaginary roots from the graphs of different equations.