SOLUTION: If you are looking at a graph of a quadratic equation, how do you determine where the solutions are?

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Question 197346: If you are looking at a graph of a quadratic equation, how do you determine where the solutions are?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

If you have a quadratic equation such as

Ax%5E2%2BBx%2BC=0

you realize that the solutions to that equation
is the solution to this system of equations:

system%28y=Ax%5E2%2BBx%2BC%2Cy=0%29

The line whose equation is y=0 is the x-axis.

So you graph the first equation, then look to
see the values of x where the graph crosses the
x-axis.

So the answer is "the x-intercepts" or
"the values of x at which the graph crosses the
x-axis.

Example:

Solve the quadratic equation:

4x%5E2-8x-21=0

The solutions to this are the x-values of the
solution to:

system%28y=4x%5E2-8x-21%2Cy=0%29

So we graph the first equation by finding
points:

(-2,11), (-1,9), (0,-21), (1,-25), (2,-21), (3,-9), (4,11)

graph%28400%2C500%2C-3%2C5%2C-26%2C12%2C4x%5E2-8x-21%29

You can see the solutions to 4x%5E2-8x-21=0
by observing that the graph crosses the x-axis
at x=-1%261%2F2 and at x=3%261%2F2.

So those are the solutions to 4x%5E2-8x-21=0.

Edwin