Let's clarify few basics before we start with Graphing Quadratic Equations.
As we know an equation of the form ax2+bx+c = 0, where a?0 is called a quadratic equation.
By solution of this equation we mean finding the values of x that satisfies this equation.
Like for x2 + 5x + 6 = 0 if you plug in x = -2 you get:
L.H.S = -22 + 5(-2) + 6 = 4 -10 + 6 =0 = R.H.S
As we get left hand side = right hand side on putting x = -2 we can say that x = -2 is the solution (root) of the equation.Similarly one can check that x = -3 is also a root of the given equation.
There are various methods to find the roots of a quadratic equation.
In this section we will concentrate on Graphing Quadratic Equations
Graphing Quadratic Equations
As a matter of fact graphing quadratic equations is not as simple as graphing linear equations. It can be tricky at times.
Mostly we are asked to graph the given quadratic equation using a graphing calculator and then interpret the roots from the graph.
Hence without getting into the details of graphing such equations we will learn to interpret the roots from the given graph.
The point to remember is: for any equation the solution of the equation is the point where the curve cuts the x-axis in its graph.
Likewise let’s take a look at the equation x2 - 5x + 6 = 0
The Graphing Quadratic Equations is given as follows :
Now from the above graph we can see that the curve cuts the x-axis at the points:
x=2 and x=3
Hence the roots of the given quadratic equation are x = 2; 3.
It is simple to interpret the above solutions as the curve cuts the x-axis at whole numbers 2 and 3.
But this may not always be the case and some sort of labelling the points in the given picture might help as shown in the further examples.
How to do Quadratic Equations Graphically
Solve the equation 0.25x2 – 0.9x + 0.1 = 0
For this picture, some points were labelled. This was quite helpful, as the x-intercepts here are not whole numbers (so we could not have guessed their values without the labels).Also the trick here was to choose the correct 2 points out of the labelled 3 points.
In short, x-values of the two points where the graph cuts the x-axis are the solutions to the equation.
The solution is x= 0.115, 3.485
Quadratic Equations Examples
Find the solution of the given quadratic.
In this example of Graphing Quadratic Equations is not given but three points are labelled.
Again here the aim is to check if you would choose the correct points. Roots are the points where the curve cuts the x-axis and not the y-axis.
The solution is x= -0.5, 1
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quadratic equations graphs , solving quadratic equations by graphs , quadratic equations graphs