Vertex representation - Examples, Exercises and Solutions

Vertex form of the quadratic equation

The vertex form allows us to identify, very easily, the vertex of the parabola and hence its name.

The vertex form of the quadratic function is:
Y=a(Xp)2+cY=a(X-p)^2+c

Suggested Topics to Practice in Advance

  1. Standard Form of the Quadratic Function
  2. Factored form of the quadratic function

Practice Vertex representation

Exercise #1

f(x)=(x3)2+x f(x)=(x-3)^2+x

Video Solution

Answer

f(x)=x25x+9 f(x)=x^2-5x+9

Exercise #2

Find the standard representation of the following function

f(x)=(2x+1)21 f(x)=(2x+1)^2-1

Video Solution

Answer

f(x)=4x2+4x f(x)=4x^2+4x

Exercise #3

Find the standard representation of the following function

f(x)=(x5)210 f(x)=(x-5)^2-10

Video Solution

Answer

f(x)=x210x+15 f(x)=x^2-10x+15

Exercise #4

Find the standard representation of the following function

f(x)=(x+5)2+3 f(x)=(x+5)^2+3

Video Solution

Answer

f(x)=x2+10x+28 f(x)=x^2+10x+28

Exercise #5

Find the standard representation of the following function

f(x)=(x+1)2+3 f(x)=(-x+1)^2+3

Video Solution

Answer

f(x)=x22x+4 f(x)=x^2-2x+4

Exercise #1

Find the standard representation of the following function

f(x)=(x+4)216 f(x)=(x+4)^2-16

Video Solution

Answer

f(x)=x2+8x f(x)=x^2+8x

Exercise #2

Find the standard representation of the following function

f(x)=(x2)2+3 f(x)=(x-2)^2+3

Video Solution

Answer

f(x)=x24x+7 f(x)=x^2-4x+7

Exercise #3

Find the vertex of the parabola

y=x26 y=x^2-6

Video Solution

Answer

(0,6) (0,-6)

Exercise #4

Find the vertex of the parabola

y=(x3)2 y=(x-3)^2

Video Solution

Answer

(3,0) (3,0)

Exercise #5

Find the vertex of the parabola

y=(x+1)2 y=(x+1)^2

Video Solution

Answer

(1,0) (-1,0)

Exercise #1

Find the vertex of the parabola

y=(x1)21 y=(x-1)^2-1

Video Solution

Answer

(1,1) (1,-1)

Exercise #2

Find the vertex of the parabola

y=(x+1)21 y=(x+1)^2-1

Video Solution

Answer

(1,1) (-1,-1)

Exercise #3

Find the vertex of the parabola

y=(x3)21 y=(x-3)^2-1

Video Solution

Answer

(3,1) (3,-1)

Exercise #4

Find the vertex of the parabola

y=x2+3 y=x^2+3

Video Solution

Answer

(0,3) (0,3)

Exercise #5

Find the standard representation of the following function

f(x)=(x6)2+2x f(x)=(x-6)^2+2x

Video Solution

Answer

f(x)=x210x+36 f(x)=x^2-10x+36

Topics learned in later sections

  1. Ways to represent a quadratic function