What is the solution of an equation?

What is the solution of an equation?

An equation consists of two terms joined by an equals sign. Your task is to solve the equation, that is, to find a number for the variable x with which both terms take on the same value.

What is the process of solving an equation called?

Solving an equation means finding all the elements of the domain that, when plugged into the equation, produce a true statement. Each such element of the domain is called the solution of the equation. One also says: A solution satisfies the equation. All solutions together form the solution set L of this equation.

How do I solve a quadratic equation?

Quadratic equations are solved with the help of the first or second binomial formula by specifically adding a number so that the binomial formula can be applied “backwards” (the so-called quadratic complement).

What do you calculate with the midnight formula?

The midnight formula is a solution formula for quadratic equations. The formula is actually called the abc formula because it solves equations of the type ax2+bx+c=0 ax 2 + bx + c = 0.

When is it a quadratic equation?

If you allow complex numbers as solutions, every quadratic equation has exactly two (possibly coincident) solutions, also called the roots of the equation. Considering only the real numbers, a quadratic equation has zero to two solutions.

When to use the PQ formula?

The PQ formula can be used to solve quadratic functions or quadratic equations. There is a common mistake here: you first have to get the equation into the form in the last graph. On the one hand we need a “= 0” and on the other hand there must be a 1 in front of x2, i.e. 1×2.

How do I know how many solutions a quadratic equation has?

Since quadratic equations can have a maximum of two real solutions, three cases are distinguished: The discriminant is greater than 0 (D>0): the quadratic equation has exactly two solutions. The discriminant is exactly 0 (D=0): the quadratic equation has exactly one solution.

What is the normal form of an equation?

Quadratic equations (equations of the 2nd degree) of the form ax² + bx + c = 0 (a≠0) can be transformed into the normal form (x² + px + q = 0) by dividing the equation by a: x2 + ba x+ about =0 . When using the “pq formula” then the following applies accordingly: p= ba and q= ca.

What is a normal form?

A normal form (also known as a canonical form) is a mathematical representation with certain properties dictated by the type of normal form. If a normal form is defined, it can be obtained from any representation using the equivalence relation.

What does the normal form say?

With the normal form you can directly read the compressedness of a parabola. Which is described by the a of y=ax2+bx+c. Also the opening direction, thanks to the sign of a. You can also read the y-axis intercept directly from c.

What is the main shape?

In the case of the main form of the straight line, the gradient k of the straight line and the ordinate section of the straight line are given. This form of representation is also called the explicit form of the straight line. This is a linear function, i.e. a vector-free form of the straight line.

How to get from vertex form to general form?

From the vertex form we come to the general form f(x)=ax2+bx+cf ( x ) = ax 2 + bx + c by removing and combining the brackets. For this, the first or second binomial formula is required.

What is the general form of a linear function?

Any linear function can be written as y is m times x plus t. Where m is the slope factor and t is the y-intercept of the line. The slope factor can be transferred to the coordinate system in the form delta y through delta x as a slope triangle.

What is the general equation of a straight line?

The general equation of a straight line is ax + by + c = 0 (where ( a ; b ) ≠ ( 0 ; 0 ) ). Every line can be described by such an equation: One chooses any line l and a point of the line M 0 as well as a vector n → orthogonal to the line, which is not the zero vector.

How do you find the equation of a straight line?

The graph of a linear function is a straight line. The equation has the form y=mx+b . Where m denotes the value for the gradient and b denotes the y-intercept.

How do I find out that a point lies on a straight line?

To find the points of a line, you plug any x-value into the equation of the line. You get the corresponding y-value. Both values ​​form the coordinates of the point lying on the straight line.

How do you set an equation of a line to vectors?

A linear equation in parameter form is generally: g:→x=→a+λ⋅→ug : x → = a → + λ ⋅ u → . Here →x is any point on the straight line, →a is the position vector of the reference point and →u is the direction vector. λ is a parameter that lengthens, shortens, or changes direction of the direction vector →u.

What is a Vectors parameter?

In mathematics, the parametric form or point direction form is a special form of a straight line equation or plane equation. In parametric form, a straight line is represented by a position vector (support vector) and a direction vector.

How do you set up an equation of a line with two points?

A straight line or a linear function is described with f(x) = y = mx + b. The variables m and b are unknown. To determine this we need two points. With this we set up two equations and solve the linear system of equations to determine m and b.

How do you make a straight line equation from 2 points?

For two given points, a straight line is to be found that goes through the points. The straight line is described by a linear function f(x) = mx + b. m and b of this function are unknown. One finds m and b by substituting the coordinates of the points into the general functional equation.

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