For the parabola Y= 9x -3x squared find the zeroes

Question

For the parabola Y= 9x-3x²

 

i) find the zeroes

ii) equation of axis of symmetry

iii) coordinates of vertex

iv) optimal value

v) Does it represent a maximum or minimum?

 

 

Thanks!

Answer 1

i)

 

Set Y=0

 

0 = 9x - 3x²

 

 

Factor the right side of equation.

 

0 = 3x(3 - x)

 

 

Set the factors equal to zero and solve.

 

3x = 0                and              3 - x = 0

 

 x = 0                                         x = 3

 

 

ii)

 

The axis of symmetry is the x coordinate of the vertex.  To find this c coordinate, we just the formula

 

x = -b / 2a

 

where:

a = -3

b = 9

 

x = -9 / (2 * -3)

 

x = 3 / 2

 

x = 1.5

 

This is the axis of symmetry.

 

 

iii)

 

To find the coordinates of the vertex, we use the formula that was used in the previous part to find the x coordinate.  Then to find the y value of the vertex, evaluate Y at the vertex's x coordinate.

 

 

iv)

 

To find the optimum, evaluate Y at the vertex.  This means what is Y when x=1.5

 

 

v)

 

The coefficient of the leading term is negative.  When this is the case, the parabola opens downward and indicates a maximum value.