Determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.
f(x) = –2x2 - 4x-8

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:

(

−

1

,

−

6

)

(

-

1

,

-

6

)

Focus:

(

−

1

,

−

49

8

)

(

-

1

,

-

49

8

)

Axis of Symmetry:

x

=

−

1

x

=

-

1

Directrix:

y

=

−

47

8

y

=

-

47

8

x

y

−

3

−

14

−

2

−

8

−

1

−

6

0

−

8

1

−

14

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

Vertex:

(

−

1

,

−

6

)

(

-

1

,

-

6

)

Focus:

(

−

1

,

−

49

8

)

(

-

1

,

-

49

8

)

Axis of Symmetry:

x

=

−

1

x

=

-

1

Directrix:

y

=

−

47

8

y

=

-

47

8

x

y

−

3

−

14

−

2

−

8

−

1

−

6

0

−

8

1

−

14

Step-by-step explanation:

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

answer: 193

explanation:

200-7 = 193