SOLUTION: Could someone please help me answer this question?
If you are looking at a graph of a quadratic equation, how do
you determine where the solutions are?
Question 177348: Could someone please help me answer this question?
If you are looking at a graph of a quadratic equation, how do
you determine where the solutions are? Found 2 solutions by gonzo, Earlsdon:Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! the roots of the equation are the value of x when y = 0.
this equates to the point where the graph crosses the x-axis.
that's why when you want to solve for the roots of a quadratic equation, you set the equation equal to 0.
if the graph doesn't cross the x-axis, then it doesn't have real roots.
in that case, it will have imaginary roots.
the values you see on the graph conform to the values you calculate.
the general form of a quadratic equation is:
to find the roots you set y equal to 0.
you get:
to find the roots, you use the formula:
if is positive, then you have real roots.
if it is negative, then you have imaginary roots.
you will only see the graph cross the x-axis if it has real roots.
here's a graph that has real roots.
the graph looks like this:
the roots are x = 5, and x = -7
here's a graph that has imaginary roots.
the graph looks like this:
the graph with imaginary roots did not cross the x-axis.
You can put this solution on YOUR website! The "solutions" or "roots" to a quadratic equation are the points on the graph of the equation where the graph (a parabola) intersects the x-axis.
Of course, some parabolas will intersect the x-axis in two places (1st. graph) in which case the equation is said to have two real roots.
Some parabolas will have their vertex just touching the x-axis (2nd graph). Such an equation is said to have double root or two identical roots.
Other parabolas will not intersect the x-axis at all (3rd graph), in which case, the equation is said to have no real roots.
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