8. Which equation is represented by the graph?

A. y = −3x^2 + 2

B. y = 2x^2 − 3

C. y = 2x^2 − 2

D. y = 3x^2 − 2

D. y = 3x^2 − 2

Step-by-step explanation:

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

Direction: Opens Down

Vertex:  

(

0

,

2

)

Focus:  

(

0

,

23

12

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

25

12

x

y

−

2

−

10

−

1

−

1

0

2

1

−

1

2

−

10

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

Direction: Opens Up

Vertex:  

(

0

,

−

3

)

Focus:  

(

0

,

−

23

8

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

−

25

8

x

y

−

2

5

−

1

−

1

0

−

3

1

−

1

2

5

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

Direction: Opens Up

Vertex:  

(

0

,

−

2

)

Focus:  

(

0

,

−

15

8

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

−

17

8

x

y

−

2

6

−

1

0

0

−

2

1

0

2

6

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

Direction: Opens Up

Vertex:  

(

0

,

−

2

)

Focus:  

(

0

,

−

23

12

)

Axis of Symmetry:  

x

=

0

Directrix:  

y

=

−

25

12

x

y

−

2

10

−

1

1

0

−

2

1

1

2

10

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1