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