# 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:
$Y=a(X-p)^2+c$

## Examples with solutions for Vertex Representation

### Exercise #1

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

### Video Solution

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

### Exercise #2

Find the vertex of the parabola

$y=x^2-6$

### Video Solution

$(0,-6)$

### Exercise #3

Find the vertex of the parabola

$y=(x-3)^2$

### Video Solution

$(3,0)$

### Exercise #4

Find the vertex of the parabola

$y=(x+1)^2$

### Video Solution

$(-1,0)$

### Exercise #5

Find the vertex of the parabola

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

### Video Solution

$(1,-1)$

### Exercise #6

Find the vertex of the parabola

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

### Video Solution

$(-1,-1)$

### Exercise #7

Find the vertex of the parabola

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

### Video Solution

$(3,-1)$

### Exercise #8

Find the vertex of the parabola

$y=x^2+3$

### Video Solution

$(0,3)$

### Exercise #9

Find the standard representation of the following function

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

### Video Solution

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

### Exercise #10

Find the standard representation of the following function

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

### Video Solution

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

### Exercise #11

Find the standard representation of the following function

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

### Video Solution

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

### Exercise #12

Find the standard representation of the following function

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

### Video Solution

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

### Exercise #13

Find the standard representation of the following function

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

### Video Solution

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

### Exercise #14

Find the standard representation of the following function

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

### Video Solution

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

### Exercise #15

Find the vertex of the parabola

$y=(x-6)^2+1$

### Video Solution

$(6,1)$