This gives us an x-coordinate of x = 4 for the vertex. We know that its x-coordinate will be the average of the zeros x = 2 ad x = 6. To do that, we can use the vertex of the parabola. First, the quadratic factored form looks like this: However, we can find the quadratic equation as well. At this point, we know that the solutions of the equation are x = 2 and x = 6. We can see from the graph that the parabola intersects the x-axis (the line y = 0) at x = 2 and x= 6.
We can sometimes find the solutions of a quadratic equation by graphing and finding the x-intercepts (zeros). Example: Solving A Quadratic Equation By GraphingĬonsider the following parabola (the graph of a quadratic): To solve a quadratic equation by graphing, all we really need to do is find out where the zeros are (the points where the graph intersects the x-axis). How To Solve Quadratic Equations By Graphing Let’s take a look at some examples of each method, starting with graphing. If r and s are real, we also have x-intercepts for the parabola, which makes it easier to graph.
However, it might be easier to factor in some cases to avoid radicals and fractions in the quadratic formula. Of course, the quadratic formula will work for any quadratic equation you choose. If factoring is hard, the quadratic formula (a shortcut for completing the square) helps. Graphing gives a good visual, but it is hard to find values of x from a graph with no equation. So, how do you solve quadratic equations? You can solve quadratic equations by graphing, factoring, completing the square, & the quadratic formula. Luckily, there are several ways to do it. Quadratic equations come up often in mathematics and physics, and it is vital to know how to solve them.