# The Vertex of the Parabola - Examples, Exercises and Solutions

## Vertex of the Parabola

The vertex of the parabola indicates the highest or maximum point of a sad-faced parabola, and the lowest or minimum point of a happy-faced parabola.

### The first method to find the vertex of the parabola: (with formula)

First step: We will find the $X$ of the vertex according to the formula $x=\frac{(-b)}{2a}$

Second step: We will place the $X$ of the vertex we have found into the original parabola equation to find the $Y$ of the vertex.

### Second method to find the vertex of the parabola: according to 2 points of intersection with the X-axis and use of symmetry

First step: Find two points of intersection of the parabola with the $X$ axis using the quadratic formula.

Second step: Find the $X$ of the vertex: the point that is exactly between two points of intersection. The calculation will be done through the average of two $X$s of the intersection points.

Third step: Place the $X$ of the vertex we have found into the original parabola equation to solve for the $Y$ of the vertex.

## Examples with solutions for The Vertex of the Parabola

### Exercise #1

The following function has been graphed below:

$f(x)=x^2-6x$

Calculate point C.

### Video Solution

$(3,-9)$

### Exercise #2

The following function has been graphed below.

$f(x)=x^2-6x+8$

Calculate point B.

### Video Solution

$(3,-1)$

### Exercise #3

The following function has been graphed below.

$f(x)=-x^2+5x+6$

Calculate point C.

### Video Solution

$(2\frac{1}{2},12\frac{1}{4})$

### Exercise #4

The following function has been graphed below:

$f(x)=x^2-8x+16$

Calculate point C.

### Video Solution

$(4,0)$

### Exercise #5

Find the vertex of the parabola

$y=x^2-6$

### Video Solution

$(0,-6)$

### Exercise #6

Find the vertex of the parabola

$y=x^2$

### Video Solution

$(0,0)$

### Exercise #7

Find the vertex of the parabola

$y=(x-3)^2$

### Video Solution

$(3,0)$

### Exercise #8

Find the vertex of the parabola

$y=(x+1)^2$

### Video Solution

$(-1,0)$

### Exercise #9

Find the vertex of the parabola

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

### Video Solution

$(1,-1)$

### Exercise #10

Find the vertex of the parabola

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

### Video Solution

$(-1,-1)$

### Exercise #11

Find the vertex of the parabola

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

### Video Solution

$(3,-1)$

### Exercise #12

Find the vertex of the parabola

$y=x^2+3$

### Video Solution

$(0,3)$

### Exercise #13

Find the vertex of the parabola

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

### Video Solution

$(6,1)$

### Exercise #14

Find the vertex of the parabola

$y=(x+2)-2$

### Video Solution

$(-2,-2)$

### Exercise #15

Find the vertex of the parabola

$y=(x+2)-3$

### Video Solution

$(-2,-3)$