![]() ![]() This slope calculator takes two points and then uses the slope formula to calculate the slope of a line defined by those two points, and then the y intercept. ![]() In order for the slope calculator to function. Is not a real number if x is negative.Your web browser must have JavaScript enabled The replacement set is the set of all non-negative real numbers, since So that the original equation is an identity. If a is any real number in the replacement set, then Since 1/x and (1- x)/x are not defined for x = 0. The replacement set for this equation is the set of real numbers except 0, Consequently this equation is an identity. Therefore, every member of the replacement set is also a member of the solution Numbers if a is any real number, then (a-1)(a+1) = a 2 -1 The replacement set is the set of all real numbers. The equation isĬonditional since, for example, 1 is a member of the replacement set but not ofĮxample 2 Consider the equation (x-1)(x+1) =x 2-1 The replacement set here is the set of all real numbers. Is satisfied by all numbers from its replacement set.Įxample 1 Consider the equation 2x-1 = x+2 Its replacement set and not satisfied by others. These numbers is a solution of its respective equation, and we will see laterĪ conditional equation is an equation that is satisfied by some numbers from We can verify by substitution that each of In the first equation above is the solution set. The set of all solutions of anĮquation is called the solution set of the equation. whileġ is a solution of the equation (x-1)(x+2) = 0. Real number 3 is a solution of the equation 2x-1 = x+2, since 2*3-1=3+2. Obviously, every solution is a member of the replacement set. Number, then the number is called a solution of the equation and is said to If an equation is true after the variable has been replaced by a specific The set of all real numbers for which all the expressions in the equation are ![]() Involving variables where the replacement set, unless otherwise specified, is In this chapter we will deal with equations This specified set of numbers is sometimesĬalled the replacement set. We recall that weĭefined a variable as a letter that may be replaced by numbers out of a given = (x-1)(x+1) are all equations that we have been using. For example, a (b + c) =ab + ac, ab = ba, and x 2-1 Each command generates a complete and detailed custom-made explanation of all the steps needed toīy an equation we mean a mathematical sentence that states that two algebraicĮxpressions are equal. X-intercepts, y-intercept, axis of symmetry and vertex of a parabola plot a parabola calculate theĭiscriminant of a quadratic equation and use the discriminant to find the number of roots of a quadraticĮquation. Rewrite a quadratic function in a different form by completing the square calculate the concavity, Quadratic equation by factoring the quadratic, using the quadratic formula or by completing the square It allows you to : factor a quadratic function (by two different methods) solve a The Quadratics page contains 13 separate commands for dealing with the most common questions concerning Go to the Equation Plotting page Quadratics Of the plot should be and what the range of the dependent variable should be.Īll equations can be given in the explicit y = f(x) form or the implicit g(x,y) Or not to show the axes, where the axes should be located, what the aspect ratio It also gives you control over such things as whether TheĪdvanced plotting page allows you to plot up to 6 equations on the one graph,Įach with their own color. Upper and lower limits on x that you want the graph to be plotted for. In order to plot a single function of x, go to the basic equation plotting page, where you can enter the equation and specify the The Plot command, from the Graphs section, will plot any function of two variables. It also allows you to eliminate certain variables The advanced command allows you to specify whether you wantĪpproximate numerical answers as well as exact ones, and how many digits ofĪccuracy (up to 16) you require. The Solve command can be uses to solve either a single equation for a single unknown from the basic solve page or to simultaneously solve a system of many equations in many unknowns from the advanced solve page. It also contains a number of special commands for dealing with quadratic equations. Even when this is not possible, QuickMath may be able to give you approximate solutions to almost any level of accuracy you require. In most cases, you can find exact solutions to your equations. The equations section of QuickMath allows you to solve and plot virtually any equation or system of equations. ![]()
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