Basically structure of quadratic equation is:
y = ax2 + bx + c.
Here a, b and c all are coefficients. We can use coefficients and equation to find vertex form from quadratic equation. In quadratic equation 'a' can never be zero because this will change the format of equation.
Step 1: First of all we have to multiply coefficient 'b' with -1. Let us take an example to understand it better. We have a quadratic equation y = x2 + 4x + 1. Here 'b' is equals to 4. So we will multiply 4 by -1 and we will get -4.
Step 2: Multiply the coefficient a with number 2. Here coefficient 'a' is 1. So we will multiply 1 with 2 which is equals to 2.
Step 3: Divide the coefficient 'b' by coefficient 'a'. This is:
-4 /2 = -2,
x = -2,
This is the value of vertex 'x' of equation.
Step 4: Now in order to find 'y' vertex we will use 'x' vertex value. We will place value of x = -2 in equation of Parabola.
Here equation is:
y = x2 + 4x + 1.
y = (-2)2 + 4(-2) + 1.
y = -3,
Vertex of parabola will have coordinates (-2, -3).