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 167757: If you are looking at a graph of a quadratic equation, how do
you determine where the solutions are?
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
If you are looking at a graph of a quadratic equation, how do
you determine where the solutions are?
----------------
If it's the usual y = a quadratic in x, it's where it crosses the x-axis.
For example:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=49 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 4, -3. Here's your graph:

If there are no real solutions, it won't cross the x-axis.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -36 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -36 is + or - .

The solution is , or
Here's your graph:
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