A graphing calculator can solve and plot various complex equations, such as parabolas and several other plotted results. They are more complex than standard calculators and sophisticated in processing various calculations and multiple equations.
Graphing calculators came about in the market in the early 1980s, intending to supplement standard calculators with fewer numerical functions.
The graphing calculator has now included functions such as the tangent, cosine sine, and the ability to display plotted graphs and solve parabola and linear equations. As a result, graphing calculators such as the slope calculator have become common tools for solving high-level mathematical courses because they present a more visual way to pursue mathematical topics.
Topics such as equations of straight lines, trigonometry, and calculus have become very easy disciplines to study. However, graphing calculators are slowly being replaced by online calculators. Below are various formulas online calculators can solve for you.
1. Slope Formula
One of the graphing formulas that an online slope calculator can solve is the slope formula. The slope is the gradient of a line; when a straight line is drawn on a Cartesian, its equation is y =mx + c. where c is the point where the line intercepts the y-axis and m is the gradient of the line, which is generally referred to as the equation of a straight line.
This is one of the main formulas a graphing calculator solves, but now its solution is available online with a slope calculator. To plot any equation in the form of Y= MX +C manually, you should make a table of x against y with at least three columns and two rows, the Xs raw and the Ys row. Then you complete the X row with value ranges according to the calibration of your graph.
Now to get the values of y, you substitute with the value of x on the table. Repeat the process until the table is complete. Upon completing the table, you can plot the x values against the y values and then join the coordinates with a ruler to obtain a straight-line graph. This process is a hassle, especially when you need a more accurate graph, which a slope calculator can easily solve.
2. Quadratic Formulas
A quadratic equation is an equation in the form of ax2 + bx + c = 0 where x is a variable, a and b are coefficients, and c is a constant. Now for any equation to satisfy a quadratic equation, the coefficient of a must not be equal to zero, that is, a ≠ 0. Quadratic equations are very applicable in our day-to-day lives, for example, solving math problems involving area, distances, relative velocities of bodies, and many more.
There are various ways of solving a quadratic equation; some of the most common ways are using the quadratic formula and the graphical method. A quadratic formula is just a simplified expression of the form ax2 + bx + c = 0, which, when simplified, becomes x = (-b±√(b²-4ac))/(2a). Quadratic equations can also be presented more visually by drawing a quadratic graph.
To do this manually, you draw a table of x against y and fill the values of x with your preferred values according to how you have labeled the x and y-axis. Substitute the values of x in the equation to obtain values of y. Repeat the process until you complete the table. Then plot the values of x against y on the graph to obtain a graph of a quadratic function.
Now where the curve intercepts, the x-axis gives the solution of x. For instance, if the quadratic function represented the motion of a moving body. The area under the curve would represent the distance covered by that body. An important thing to note when plotting graphs of quadratic functions is that if the coefficient of a is a positive number, the function should curve upwards.
And if the coefficient is negative, the function should curve downwards. However, a graphing calculator can easily solve all these quadratic expressions. Like there are online slope calculators, there are online calculators that can solve quadratic formulas and plot the graph.
3. Area Formulas
You don’t have to cram a batch of formulas to find the area of various common geometric figures. An online calculator will ease you from that. All you have to do is choose the geometric figure you want to find the area. And then, input the dimensions and click calculate; you will get the answer within milliseconds.
Online calculators such as slope calculators perform a function of a graphing calculator by helping you to find the area under the graph and many other graphical solutions. An online calculator will also help you find the area under various polynomial functions, such as quadratic and cubic equations.
4. Trigonometric Formulas
Trigonometry is a branch of mathematics that deals with various functions of angles, the associated calculations, and their applications. The common angle functions are tangent, cosine, sine, cosecant, secant, and cotangent. One of the key advantages of graphing calculators over standard calculators is the ability to solve trigonometric equations and plot graphs of trigonometric functions.
But the good thing is that you don’t have to own a graphing calculator to solve various trigonometric functions because online calculators, such as slope calculators, can solve tangent functions.
For example, the gradient of a line through the origin is given by a change in y coordinates divided by the change in x coordinates which is the same as height/base. In trigonometric ratios, height/base is the same as tanθ, equal to the gradient. Therefore, the gradient obtained by the slope calculator is equal to tanθ when plotted on a Cartesian plane.
With an online calculator, you don’t need to use a graphing calculator; this is because the calculator can perform all the functions done by a graphing calculator. Some of the formulas an online calculator can solve include the slope formula, which can easily be done using a slope calculator, and quadratic formulas, used to solve all quadratic expressions.
An online calculator also has various formulas to find the area of common geometric figures by just inputting the dimensions. The calculator can also find the area under the various functions, which helps us understand what the function depicts. There is also no need for a graphing calculator because online calculators can solve various trigonometric ratios, functions, and other trigonometric formulas.