Solve Equations to Vertex Form

Solve equations to vertex form article deals with how to write the standard equation to vertex form and the model problems that helps to understand vertex form.

General form of equation and vertex form:

For solving equation to vertex form, we should have idea in general form

1. The general form of the quadratic function is f(x) =ax2+bx+c

2. The general form of the vertex equation is

f(x) = a(x-h)2 +k

Here (h, k) is the vertex.
Steps in Solving Equations to Vertex Form:

In solving the equation tovertex form, the following steps are very important

Step1: First, we need to factor out the leading coefficient.

Step2:  Add and subtract by common number `(b/2) ^2`

Step 3: simplify the equation to the vertex form.
Model Problems to Solve Equation to Vertex Form:

1. Solve the equation to vertex form f(x) = 2x2 +8x +35.

Solution:

Let f(x) be y

y= 2x2 +8x +35.

Step1: First, we need to factor out the leading coefficient

y = [2x2 +8x]+35
y = 2[x2 +4x]+35

Step2:  add and subtract by common number `(b/2) ^2`

y = 2[x2 +4x + (2)2 -(2)2]+35

Step 3: simplify the equation to the vertex form.

y = 2[(x2 +4x + 4] +35-8
y= 2[(x +2)2] +35-8

y = 2[(x +3)2] +27

Here the vertex form is y =2[(x +3)2] +27 , vertex is (-3,27)

2. Solve the equation to vertex form f (x) = x2+4x+21

Solution:

Let f(x) be y

y= x2+4x+21

Step1: First, we need to factor out the leading coefficient

y = (x2+4x) +21

y = (x2+4x) +21

Step2:  add and subtract by common number `(b/2) ^2`

y = (x2+4x+4) +21-4

Step 3: simplify the equation to the vertex form.

y = (x2+4x+4) +17

y = (x+2)2+17

Here the vertex form is f(x) = (x+2)2+17, vertes is(-2,17)

3. Solve the equation to vertex form y= x2+16x+30

Solution:

y= x2+16x+30

Step1: First, we need to factor out the leading coefficient

y= (x2+16x) +30

y= (x2+16x) +30

Step2:  add and subtract by common number `(b/2) ^2`

y= (x2+16x+64) +30-64

Step 3: simplify the equation to the vertex form.

y= (x2+16x+64)-34

y= (x+8)2-34

Here the vertex form is f(x) = (x+8)2-34, vertex is (-8,-34)