f(x)= -(x-1)(x-6) Find x-intercepts and maximum height of graph

Question

first find x- intercepts then find the max height 

Answer 1

f(x) = -(x-1)(x-6)

Replace f(x) with y

y = -(x-1)(x-6)

 

x intercepts occur where the value of

y = 0

That is at x = 1 and x = 6

x intercepts are (1,0) and (6,0)

 

To find the maximum multiply out the

equation to form the quadratic:

 

-(x-1)(x-6) = -(x²-7x+6) = -x²+7x-6

 

y = -x²+7x-6

This graphs as a parabola opening downward.

The maximum height is the y value at the 

vertex of the graph.

The x coordinate of the vertex is -b/2a

from quadratic equation.

a=-1, b=7, c=-6

-b/2a = -7/(-2) = 7/2

 

Note: the x coordinate of the vertex is

the midpoint of the x intercepts:

Halfway between 1 and 6 is 3 1/2 or 7/2

 

To find the maximum height replace x

with 7/2 in y=-x²+7x-6 and solve for y

Answer 2

x-intercepts: (1, 0) and (6, 0)

maximum occurs at x = 3.5

 

Can you calculate the maximum?