feed-o-math

Graphing a quadratic equations is a big challenge for most of you , we bring the methods to draw their graphs on the go.

In the previous post in which we talked about finding the roots of a equation, we talked about the sum and products of a quadratic , now the proof to them is what we will be learning here.

The most important thing about any polynomial are its roots. In this post we are going know the four ways of finding the roots of a quadratic equation. Lets understand first what roots mean for any equation in x. Graphically, These are points where the graph of that expression in x cut or touch the x axis which is obvious as theoretically we studied that root is the point where the expression gives y=0 and for any point on graph with y=0 it lies of x axis. Lets see some examples- It has two roots It has 1 root It has no root By counting the number of points where the graph cuts or touches the x axis gives us the number of roots possessed by that equation. Now lets see the ways in which we can solve to find the roots of quadratic equation - 1. Middle Term Splitting method- This method follows a protocol and it not easy for some equation to apply this however in most places it is applicable. Lets take an example 2 x 2  + 3x - 2 = 0 Step 1: Compare this with the standard equation i.e.   a

In this post we will be going to study about quadratic equations. Quadratic equations are those equations which have overall degree to be 2. The general form for any quadratic equation in x is - ax 2  + bx + c = 0 ,  where  a ≠ 0 The graph of this kind of equations are parabolas. The equations has degree two hence it will have atmost two real roots. What are roots? Roots or zeroes are the values of x for which the polynomial  P(x)  =  ax 2  + bx + c  becomes equal to zero. We should be very careful about the fact that a quadratic equation has maximum of two real roots . There are three  four ways to find the roots of a quadratic equation which we will learn in upcoming posts. 1. Middle term splitting. 2. Completing the square. 3. Using Sridharacharya Formula or Quadratic formula. 4. A differeent way.(by Po-Shen Loh ) Stay Tuned  for the next post. For any query comment down there. #graphs_on_the_go  # understanding_graphs #mathematics, #feed-o-math , #quadratic_equations

In this post we will learn what happen when we apply modulus at y.

In this post we are going to know about the effect modulus (| |) has on any graph.

Knowing how to sketch straight lines is very important if belong Mathematics and Science. How to sketch straight lines? The standard equation of a straight line is ax + by + c = 0 There are basic 5 forms of line's equation. In order to understand all the five we must know some of the basic terms we will be frequently using- Slope of a line: Slope of a line defines the tangent(tan of trigonometry) of the angle at which the line is inclined with the +ve x axis.      Above mentioned are three ways to find the slope of a line. slope is generally represented by m.                                                                                             Y-intercept:  The intercept cut by the line with y axis. It is represented by c. Let's come back to the 5 forms of equation of line- 1. One point slope form 2. Two point slope form 3. Slope intercept form 4. Intercept form 5. Normal form 1. One point slope form:   (y - y1) = m(x-x1) In this we need one point (x1,y1) and slope of th

After reading the title a question must have arose to your mind that , "does adding or subtraction a constant to a function different than that for x ?". The answer is YES. Let's begin. As always lets start with an example say y = x^2 and change this to y = (x+2)^2. Now what does this addition of 2 in x make change to the function. Let's Examine. x = 0, y = 0 (original) x = 0, y = (0+2)^2 = 2^2 = 4 (modified) Lets take another example- x = 4, y = 16 (original) x=4 , y = (4+2)^2 = 6^2 =36 (modified) it means modified function should shift 2 unit left on x axis. lets see the graphs and make it clear. the original function shifts left to number of units added to x along x-axis. Now let's take an example if 2 is subtracted to from the original function. Taking the same example y = x^2 and y = (x-2)^2 Let's Examine. x = 0, y = 0 (original) x = 0, y = (0-2)^2 = (-2)^2 = 4 (modified) Lets take another example- x = 4, y = 16 (original) x=4 , y = (4-2)^2 = 2^2 = 4 (mod

Hope you all have gone through the basic graphs. In this post we will modify those graphs. Let's begin............ Let's take a graph say y = x^2. Now if we add 2 in it which means if we change the function to y = x^2 + 2 Then, the resultant graph looks like the second graph.                                actually what happened is the original graph adds 2 to its each value. For example it was giving y=4 at x=2 But now it gives y=4+2=6 at x=2 Similarly if we would have taken y = x^2 -2 Then the graph would have decreased 2 from each value of y.. Example- for x=2 it gave y=4 originally but now for x= 2 it will give y= 4-2=2. The resultant graph will look like-                                   Similarly some other examples where constants are added or subtracted in a particular function are as follows- (where k>0 and k belongs to Real numbers)            Stay Tuned  for the next post. For any query comment down there. #graphs_on_the_go  # understanding_graphs #mathematics, #