Let us analyze the graph and answer the given questions.

Observations from the graph:

The quadratic graph opens upwards, indicating a minimum turning point.

Answers:

a) The coordinates of the $y$-intercept: The $y$-intercept is where the graph crosses the $y$-axis. From the graph, this happens at: $(0, -3)$

b) The coordinates of the turning point: The turning point is the vertex of the parabola, which is at the lowest point of the graph. From the graph, this occurs at: $(3, -5)$

c) The roots of the function: The roots of the function are the $x$-intercepts, where the graph crosses the $x$-axis. From the graph, these are: $x = 1 \quad \text{and} \quad x = 5$

Final Answers:

1. $y$-intercept: $(0, -3)$
2. Turning point: $(3, -5)$
3. Roots: $x = 1$ and $x = 5$

Would you like a detailed explanation or further clarification on how to interpret such graphs?

5 Related Questions:

1. How can you determine the equation of the quadratic function using the graph?
2. What is the axis of symmetry of this parabola, and how is it related to the turning point?
3. How can you calculate the distance between the roots of the quadratic function?
4. How does the $y$-intercept help in identifying the constant term in the quadratic equation?
5. What transformations (shifts or stretches) could produce this parabola from $y = x^2$?

Tip:

When analyzing quadratic graphs, always identify key features like intercepts, turning points, and symmetry to extract the equation or understand its properties