How do you find the axis of symmetry, and the maximum or minimum value of the function f(x)=x^2 -2x -15?

2 Answers

Axis of symmetry x=1
Minimum value =-16

Explanation:

The parabola opens upward and so this function has a minimum value.
To solve for the minimum value we solve for the vertex.

y=ax^2+bx+c

y=1*x^2+(-2)*x+(-15)

so that a=1 and b=-2 and c=-15

Vertex (h, k)

h=(-b)/(2a)

h=(-(-2))/(2(1))=1

k=c-b^2/(4a)

k=-15-(-2)^2/(4(1))

k=-15-1

k=-16

Vertex (h, k)=(1, -16)

The minimum value of the function is f(1)=-16

Kindly see the graph of f(x)=x^2-2x-15 with the axis of symmetry x=1 dividing the parabola into two equal parts.
graph{(y-x^2+2x+15)(y+1000x-1000)=0[-36,36,-18,18]}

God bless ....I hope the explanation is useful.

May 4, 2016

Axis of symetry x=1
Value of the function y=-16

Explanation:

Given -

y=x^2-2x-15

Find Axis of symetry.

x=(-2b)/(2a)=(-(-2))/(2 xx 1)=2/2=1

Axis of symetry x=1

Maximum of Minimum Values

dy/dx=2x-2
(d^2y)/(dx^2)=2
dy/dx=0 =>2x-2=0
x=2/2=1

At (x=1): dy/dx=0;(d^2y)/(dx^2)>0
Hence there is a minimum at x=1

Value of the function

y=1^2-2(1)-15
y=1-2-15=-16