How do the solutions to an equation relate to the graph of the equation?

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answers:
Jeffrey K say: Each point where the graph crosses the x axis is a solution.
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electron1 say: Let me give you some examples. A car is moving a constant speed. The following equation us used to determine the distance is has moved at specific time.

d = v * t
The graph of this equation is straight line. The car’s velocity is the slope of the line. To prove that this true, let the velocity be 30 m/s and the times be 2, 3, and 4 seconds.

d1 = 30 * 2 = 60 meters
d2 = 30 * 3 = 90 meters
d3 = 30 * 4 = 120 meters

Now let’s assume the car’s velocity is increasing. The acceleration is 5 m/s^2. The following equation us used to determine the distance is has moved at specific time.

d = vi * t + ½ * a * t^2, vi = 0 m/s
d1 = ½ * 5 * 2^2 = 10 meters
d2 = ½ * 5 * 3^2 = 22.5 meters
d3 = ½ * 5 * 4^2 = 40 meters

If you graphed distance versus time, the graph would be a parabola. If you go to the website below, you will see these two graphs.

https://opentextbc.ca/physicstestbook2/c...

I hope this is helpful for you.
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az_lender say: There is no such thing as "the graph of an equation."

If the equation has a zero on one side, the function on the other side can have a graph, and the solutions of the equation are the points where the function's graph crosses the x-axis.
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Morningfox say: The solutions tell you where the graph cross the X-axis.
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