```Question 244875
first of all, you need the equation to get the graph.

the graph give you a visual representation of the relationship between your  variables.   this is helpful if you are unsure as to what type of relationship is represented by the equation.  it can also help you narrow down what your solutions to the equation need to be.

the equation provides you with the detailed information you need to obtain.

as an eqample:

quadratic equation is x^2 + x - 6

you would see the following:

{{{graph(600,600,-10,10,-10,10,x^2 + x - 6)}}}

at a glance, you can see that this looks like a parabola that opens upward and that passes the x-axis at two points and that it has a minimum point at somewhere between 6 and 7.

you might not know the exact values, but you know the vicinity they are going to be in.

when you solve the equation, you get the detailed numbers for the roots and for the minimum point on the graph.

the graph gave you an idea.

solving the equation and comparing it to the graph confirmed whether your solution was accurate or not.

in general, the graph is not capable of providing you with the exact details because the accuracy of the graph presentation and your ability to see very fine details do not compare to the accuracy of solving the equation.

graph provide you with a visual representation, but sometimes that presentation is not what is really happening.

take a sine wave for the cycles of alternating current of electricity.

the graph shows the electricity going through several cycles but shows it in a linear fashion.

the curve goes from left to right.  it goes up and then down and then up and then down as it travels to the right.

in reality the alternating current is going back and forth over the same wire.

the graph is not visualizing reality but once you learn to translate reality to what the graph is showing you, then you can understand what is going on.

in mathematics, the graph visualizes for you what is happening which helps you to see more clearly what the equation is doing for you.

they work together.

one can't replace the other.

they both support each other.

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