Question

Graph the function. Label the axis of symmetry, vertex, y-intercept, increasing and decreasing intervals.

G(x) = - 3x^2+ 6x - 2
Axis of symmetry:
Vertex:
Y-intercept:
Increasing:
Decreasing:

Answer 1

The graph the function represented by the equation g(x) = -3x² + 6x - 2 is attached

Axis of symmetry: x = 1

Vertex: (1, 1)

Y-intercept: (0, -2)

Increasing: (-∝, 1)

Decreasing: (1, ∝)

How to graph the function represented by the equation

From the question, we have the following parameters that can be used in our computation:

g(x) = -3x² + 6x - 2

The axis of symmetry is calculated as

x = -b/2a

So, we have

x = -6/(2 * -3)

x = 1

Next, we have the y-coordinate of the vertex to be

g(1) = -3(1)² + 6(1) - 2

g(1) = 1

So, the vertex is (1, 1)

For the y-intercept, we have

g(0) = -3(0)² + 6(0) - 2

g(0) = -2

Lastly, the increasing and decreasing intervals are (-∝, 1) and (1, ∝), respectively

The graph is attached