Question

Identify the graph of g(x)=2(x+3)^2

Answer 1

Answer
The graph will have a vertex of ( -3, 0 )
The y intercept is at 18

Step by step

2(x + 3)^2
Is the same as
2( x + 3) (x + 3)
Multiply parentheses first
2 ( x^2 + 6x + 9)
Distribute multiply the 2

2x^2 + 12x + 18 is your standard equation

Our y intercept is 18

*Since we know (0, 18) is our y intercept and our axis of symmetry is -3, we can plot another point at ( -6, 18) to draw our parabola

To find the x of the vertex
x = - b/2a
x = - 12/(2)(2)
x = - 12/4
x = -3

Sub -3 for x in equation 2x^2 + 12x + 18

(2)(-3)^2+ (12)(-3) + 18
(2)( 9) + ( -36) + 18
18 -36 +18
y = 0

Vertex is at ( -3, 0 )

Graph is attached

Answer 2

Explanation:

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

Direction: Opens Up

Vertex:

(

3

,

0

)

Focus:

(

3

,

1

4

)

Axis of Symmetry:

x

=

3

Directrix:

y

=

−

1

4

x

y

1

4

2

1

3

0

4

1

5

4

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