**The formula and its examples.**

To kick off, a few words about the subject of mathematics. Mathematics is a difficult subject: formulas, numbers and other departments that entail years of study. However, to get to grips with more difficult mathematical examples, we have to know the basics. The basics are not so difficult but, if you don't know them, you can't move on to difficult tasks and solve them.

The basic starting point for a quadratic equation is the formula: ax2 + bx + c = 0. However, the formula for the delta is as follows: Δ = b2 + 4ac. Vieta's formulas are also important in this section: x1 + x2= - ba and x1 * x2 = ca.

Example: 3x2 + 4x = 5 Δ = 42 - 4 * 3 (-5) = 16 + 60 = 76

3x2 + 4x - 5 = 0 √Δ=76 = √4*19 = 2√19

a=3, b= 4, c = -5 x1= -2-√19 /3

x2=-2+√19/3

**Graph of the function - quadratic inequalities**

A quadratic inequality, conversely, is represented by a graph. Its method consists of transferring, with sign, the data given in the example. In this manner, we obtain the formula of the quadratic function. Calculate the root of delta from the formula then substitute it into the formula to obtain the zero places.

Mark these zeroes on the graph. In this way, you can obtain a parabola. There is no equals sign. However, there are lesser, greater, positive, zero values.

Example:

f(x) = x2 + 4x +3

Δ=44 + 4*1*3 = 16 - 12 = 4

√Δ = 2

x1 = -3, x2 = 1

We read the equation from the graph (which should be sketched beforehand) and mark the values that are in the given interval on it.

In conclusion, **quadratic equations and quadratic inequalities have two separate methods. In addition**, you can't calculate these measures without using formulas and the basics of mathematics.

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