The vertex form of the equation is , that is .
Step-by-step explanation:
A quadratic equation is a two degree equation that has the standard form .
The degree of the given equation is therefore it is a quadratic equation.
Every quadratic equation represents a parabola so the given equation also represents a parabolic function.
The standard form of equation of a parabola is written as shown below.
Here, the value of represents whether the parabola is upwards or downward and the point is the vertex of the parabola.
Therefore, the above equation form is known as the vertex form of the equation.
To transform any quadratic equation into its vertex form, we use completing the square method.
Firstly, if the coefficient of is other than then divide the complete equation by that coefficient.
Here, the coefficient of is so the first step is not required.
Now, add a value and subtract the same value such that it forms a perfect square.
For a standard quadratic equation , the value that is added and subtracted in the expression is calculated as .
Hence, add and subtract to the equation and simplify as shown below.
Therefore, the vertex form of the equation is .
Learn more:
1. General form of equation of a circle brainly.com/question/1506955
2. Domain and range of a function brainly.com/question/3412497
3. Coordinate geometry brainly.com/question/7437053
Answer details
Grade: Middle school
Subject: Mathematics
Chapter: Quadratic equation
Keywords: equation, vertex form, quadratic equation, parabola, vertex, coefficients, add, subtract, divide, standard form, simplify, completing the square, vertex point, degree.