Identify the vertex and the axis of symmetry of the graph of the function y=3(x + 2)² - 3

Solution:

Given, the function is y = 3(x + 2)² - 3 ---------- (1)

We have to identify the vertex and the axis of symmetry of the function.

The equation of the parabola in vertex form is given by

y = a(x - h)² + k ------------ (2)

Where, (h, k) is the vertex

Comparing (1) and (2),

a = 3

h = -2

k = -3

Vertex, (h, k) = (-2, -3)

The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.

The axis of symmetry always passes through the vertex of the parabola.

x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

So, the axis of symmetry is x = -2

Therefore, the vertex is (-2, -3) and the axis of symmetry is x = -2.

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Identify the vertex and the axis of symmetry of the graph of the function y = 3(x + 2)² - 3

Summary:

The vertex and the axis of symmetry of the graph of the function y = 3(x + 2)² - 3 is (-2, -3) and x = -2.