# What is the the vertex of #y = 1/2(x+1)(x-5) #?

##### 3 Answers

vertex:

#### Explanation:

**Note:**

Vertex form

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

#h= x_(vertex) = -b/(2a) " " " "# ;#k= y_(vertex)= f(-b/(2a))#

**Given:**

#y= 1/2 (x+1)(x-5)#

Multiply the expression or FOIL

#y = 1/2(x^2 -4x-5)#

#y= 1/2x^2 -2x -5/2#

#a = 1/2;" " b= -2;" " " c= -5/2#

#color(red)(h= x_(vertex)) = (-(-2))/(2*1/2) =color(red) 2#

#color(blue)(k= y_(vertex)) = f(2) = 1/2(2)^2 -2(2) -5/2 #

#=> 2-4 -5/2 => -2 -5/2 => color(blue)(-9/2 #

The vertex form is

#### Explanation:

First, find the expanded form of the quadratic.

Now, the vertex of a parabola can be found with the vertex formula:

Where the form of a parabola is

Thus,

The

The

Thus, the vertex of the parabola is

You can check the graph:

graph{1/2(x+1)(x-5) [-10, 10, -6, 5]}

#### Explanation:

This is a quadratic thus of the hors shoe type shape.

That means that the vertex is

The x-intercepts will occur when y=0

If y is 0 then the right side also = 0

The right side equals zero when

For

For

Half way is

Having found