State where the graph of the parabola is increasing and where it is decreasing.

Question

State where the graph of the parabola is increasing and where it is decreasing.

 

        2

y = x   - 10x

 

 

1. State where the graph of the parabola is increasing.

 

x < or > = ?

 

2. State where the graph of the parabola is decreasing.

 

x < or > = ?

 

Answer 1

Hi Keith;

y=x²-10x

The parabola opens upward.  We know this because x² has a positive coefficient.

Let's establish the vertex of the parabola...

The vertex is -b/2a

--10/[(2)(1)]

5

x=5

y=(5)²-[(10)(5)]

y=25-50

y=-25

vertex...(5,-25)

This is the point-of-symmetry, the lowest point of the parabola.

There is no value of y lower than -25.

For all values of x lower than x=5, the values of y are increasing.

For all values of x higher than x=5, the values of y are also increasing.

Otherwise, I do not understand the question.

 

Answer 2

y = x^2 - 10x = x(x-10)

 

Zeros are x = 0 and x = 10. Axis of Symmetry is x = 5.

 

Vertex is (5,y(5)) = (5,-25).

 

-25 is the minimum value of the function because it's opening up,

 

so the function is decreasing for x < 5 and increasing for x > 5.