Education

Vertex Form: Building a Foundation in Algebra

Mathematics is a subject of learning that is both very interesting and complicated for most people. The interesting side of mathematics is when they are able to provide a way out for many of the confusion that scientists face, one of which is in the discussion of vertex form.

The vertex formula itself is nothing new, where in the world of formal education in general; this material has been taught a lot and has become one of the very solid foundations in building an algebraic formula. If there was no knowledge of this, algebra might not have been discovered and studied until now.

What is Vertex Form?

The vertex formula is widely used to find the coordinates of a point where a curve intersects its symmetry axis. The peak is called the vertex (h, k). For those of you who have formal education or who are particularly concerned with the subject of mathematics, of course you already know that the standard equation for calculating a curve is: y = ax 2 + bx + c.

In this formula, if the x2 coefficient has a positive shape, then the vertex of the curve is at the bottom of a U-shaped curve. However, if the coefficient is negative, then the vertex on the curve is at the top of a U-shaped curve.

The peak at a minimum curve is when the curve is in an open position upwards, or a maximum curve is when the curve is open downwards, and for a curve the position rotates or has changed its direction.

How to Find the Vertex of Curve

So that we can find a vertex on a curve, there is one way to use a graph that will help in finding the maximum and minimum values on the curve.

It can also use two points or use symmetry on the curve. You can also use a quadratic equation with the appropriate formula. You will find the vertices of a curve through the formulas of quadratic equations that have the form of factored form, vertex, or standard form.

Finding the Vertex of the Curve

There are several ways to find the vertex of a curve, understand this theory carefully and if necessary read it several times so that you can understand its application correctly and remember it at any time:

Through the use of equations: By using a system of quadratic equations with factored form, vertex form, and standard form, it will be possible to find the vertices of the required curve.

Using the two-point or symmetry method: You can use any two points that are on a horizontal line that are the same distance as you measure from the vertex of the curve. It can also take advantage of symmetry in order to find the peak point.

Utilizing graphs: By using a quadratic graph, you can see the local maximum or the shape of the top of the curve, and also the local minimum or the shape of the bottom of the curve to be able to find points at the top of the curve.

Read also : How Math Improves Your Critical Thinking

Relationship with Algebra

Vertex is applied also in algebra. As already explained, the curve is a graph of an equation with a shape like the letter U. The curve is generated from a quadratic equation which can be used as a variation of the following formula:

y = ax2 + bx + c y = ax^2 + bx + cy = ax2 + bx + c

There are two types of parabolic apex, there is a point under the letter U when it opens upwards, it can also be at the top point of the letter U that opens downwards or U is upside down.

For example, the bottom point of the curve has the equation y = x2 with the point position (0,0). There are rising charts on either side of this point. It can be concluded (0,0) to be the peak and vertex of the graph from the equation y = x2.

The formula for finding the vertex of a curve using many methods is a solid foundation in an equally interesting subject of algebra.

What is Algebra?

Algebra is referred to as a form of branch of knowledge in mathematics and discusses in detail how to simplify as well as solve problems using symbols as substitutes.

The forms are constants and variables. This subject is known as a branch of mathematics which discusses the theory of geometry, numbers, and algebraic theory to conduct research.

That is why the vertex form is an important first step to create a strong foundation in the world of mathematics education.

Algebra Inventor

Muhammad Ibn Musa Al-Khwarizmi was born in Bukhara in 780 AD, lived in Khawarizmi for a long time and he really liked mathematics as a challenging knowledge.

Al-Khwarizmi was one of the researchers who discovered algebra, marked by the large library and scientific research center created by Harun Al-Rashid. Al-Khwarizmi was known to many Europeans as Algorizm or is now known as the algorithm concept. The concept of algorithm has been used in various types of science, related to computers and engineering.

That is a discussion of the relationship between Vertex form which is a strong foundation in the world of algebra that is widely used today. Algebra has provided many benefits in technological developments because its formulation is widely used in computerized programs and is also associated with coding and the creation of software or applications that are commonly used today.