Question

What is the relationship between the “solution” to a quadratic equation and the graph of a quadratic equation? How many possible real solutions might there be when you solve a quadratic equation and how do these possible solutions affect the position the parabola on a coordinate plane?

Answer 1

The solutions of a quadratic equations are the x value of the x-intercepts of the graph. 

If there are 0 real solutions, the parabola will not touch the x-axis.

If there is 1 real solution, the parabola's vertex will be on the x-axis.

If there are 2 real solutions, the parabola will intersect the x-axis in two distinct positions.

Hope this helps!

Answer 2

The solutions of the quadratic equation are the x-values at which the graph intercepts the x-axis.

What are the solutions of a quadratic equation?

We usually say that a quadratic equation is something like:

ax^2 + bx + c = 0.

This equation will have solutions that only depend on a, b, and c.

While for the graph of a quadratic equation, we have:

y = ax^2 + bx + c

The relation between the solutions and the graph, is that the solutions are the values of x at which the graph intercepts the x-axis.

And if there is no intercept, then we have no real solutions.

If you want to learn more about quadratic equations, you can read:

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