We are given the graph of a quadratic function (a parabola). We need to determine the following: a) The codomain of the function. b) The zeros of the function. c) The y-intercept (ordinate at the origin). d) The equation of the axis of symmetry. e) The intervals of increase and decrease of the function.

1. Problem Description

We are given the graph of a quadratic function (a parabola). We need to determine the following:

a) The codomain of the function.

b) The zeros of the function.

c) The y-intercept (ordinate at the origin).

d) The equation of the axis of symmetry.

e) The intervals of increase and decrease of the function.

2. Solution Steps

a) Codomain of the function: From the graph, we can see that the highest y-value the function reaches is -

3. The parabola opens downwards, so the codomain consists of all y-values less than or equal to -

3. Therefore, the codomain is $y \le -3$.

b) Zeros of the function: The zeros of the function are the x-values where the graph intersects the x-axis (where $y = 0$). From the graph, the function intersects the x-axis at $x = -2$ and $x = 2$.

c) y-intercept (ordinate at the origin): The y-intercept is the y-value where the graph intersects the y-axis (where $x = 0$). From the graph, the function intersects the y-axis at $y = -4$.

d) Equation of the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex of the parabola. The x-coordinate of the vertex is the midpoint of the zeros. The zeros are -2 and 2, so the x-coordinate of the vertex is $\frac{-2 + 2}{2} = 0$. Therefore, the equation of the axis of symmetry is $x = 0$.

e) Variation of the function: The function is increasing to the left of the vertex and decreasing to the right of the vertex. The vertex is at $x = 0$.

The function is increasing for $x < 0$ and decreasing for $x > 0$.

3. Final Answer

a) Codomain: $y \le -3$

b) Zeros: $x = -2$ and $x = 2$

c) y-intercept: $y = -4$

d) Axis of symmetry: $x = 0$

e) Increasing for $x < 0$ and decreasing for $x > 0$