Vertex Representation - Examples, Exercises and Solutions

Question Types:
Vertex Representation: Transition between different representations of a functionVertex Representation: Linking function properties to its representation

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(X−p)2+cY=a(X-p)^2+c

Detailed explanation

Suggested Topics to Practice in Advance

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

Practice Vertex Representation

Question 1

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

Question 2

Find the standard representation of the following function

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

Question 3

Find the standard representation of the following function

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

Question 4

Find the standard representation of the following function

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

Question 5

Find the standard representation of the following function

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

Examples with solutions for Vertex Representation

Exercise #1

f(x)=(x−3)2+x f(x)=(x-3)^2+x

Video Solution

Answer

f(x)=x2−5x+9 f(x)=x^2-5x+9

Exercise #2

Find the standard representation of the following function

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

Video Solution

Answer

f(x)=x2−2x+4 f(x)=x^2-2x+4

Exercise #4

Find the standard representation of the following function

f(x)=(x−2)2+3 f(x)=(x-2)^2+3

Video Solution

Answer

f(x)=x2−4x+7 f(x)=x^2-4x+7

Exercise #5

Find the standard representation of the following function

f(x)=(x+4)2−16 f(x)=(x+4)^2-16

Video Solution

Answer

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

Question 1

Find the standard representation of the following function

\( f(x)=(x-5)^2-10 \)

Question 2

Find the standard representation of the following function

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

Question 3

Find the vertex of the parabola

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

Question 4

Find the vertex of the parabola

\( y=(x-1)^2-1 \)

Question 5

Find the vertex of the parabola

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

Exercise #6

Find the standard representation of the following function

f(x)=(x−5)2−10 f(x)=(x-5)^2-10

Video Solution

Answer

f(x)=x2−10x+15 f(x)=x^2-10x+15

Exercise #7

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 #8

Find the vertex of the parabola

y=(x+1)2−1 y=(x+1)^2-1

Video Solution

Answer

(−1,−1) (-1,-1)

Exercise #9

Find the vertex of the parabola

y=(x−1)2−1 y=(x-1)^2-1

Video Solution

Answer

(1,−1) (1,-1)

Exercise #10

Find the vertex of the parabola

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

Video Solution

Answer

(−1,0) (-1,0)

Question 1

Find the vertex of the parabola

\( y=x^2+3 \)

Question 2

Find the vertex of the parabola

\( y=x^2-6 \)

Question 3

Find the vertex of the parabola

\( y=(x-3)^2-1 \)

Question 4

Find the vertex of the parabola

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

Question 5

Find the standard representation of the following function

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

Exercise #11

Find the vertex of the parabola

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

Video Solution

Answer

(0,3) (0,3)

Exercise #12

Find the vertex of the parabola

y=x2−6 y=x^2-6

Video Solution

Answer

(0,−6) (0,-6)

Exercise #13

Find the vertex of the parabola

y=(x−3)2−1 y=(x-3)^2-1

Video Solution

Answer

(3,−1) (3,-1)

Exercise #14

Find the vertex of the parabola

y=(x−3)2 y=(x-3)^2

Video Solution

Answer

(3,0) (3,0)

Exercise #15

Find the standard representation of the following function

f(x)=(x−2)2+4 f(x)=(x-2)^2+4

Video Solution

Answer

f(x)=x2−4x+8 f(x)=x^2-4x+8

Topics learned in later sections

  1. Ways to represent a quadratic function