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The given equation is \( y = (x - 1)(x - 3) \). This is a quadratic equation that represents a parabola. Let's solve for the required coordinates step by step:

### a) Coordinates of points A and B
Points \( A \) and \( B \) are the x-intercepts, which are found by setting \( y = 0 \) in the equation:

\[
(x - 1)(x - 3) = 0
\]

This gives two solutions:
- \( x = 1 \)
- \( x = 3 \)

Thus, the coordinates of \( A \) and \( B \) are:
- \( A = (1, 0) \)
- \( B = (3, 0) \)

### b) Coordinates of point P
Point \( P \) is the y-intercept. To find the y-intercept, we set \( x = 0 \) in the equation:

\[
y = (0 - 1)(0 - 3) = (-1)(-3) = 3
\]

Thus, the coordinates of \( P \) are \( (0, 3) \).

### c) Coordinates of the turning point Q
The turning point of a parabola can be found by calculating the midpoint of the x-intercepts (A and B), which gives the x-coordinate of the vertex.

The x-coordinate of the turning point is:
\[
x = \frac{1 + 3}{2} = 2
\]

To find the y-coordinate of the turning point, substitute \( x = 2 \) into the equation:

\[
y = (2 - 1)(2 - 3) = (1)(-1) = -1
\]

Thus, the coordinates of the turning point \( Q \) are \( (2, -1) \).

### Final answers:
- \( A = (1, 0) \)
- \( B = (3, 0) \)
- \( P = (0, 3) \)
- \( Q = (2, -1) \)

Would you like a more detailed explanation on any of these steps?

Here are 5 related questions you might be interested in:
1. How do you find the axis of symmetry for a parabola?
2. What is the significance of the turning point in a quadratic graph?
3. How can you determine if a parabola opens upwards or downwards?
4. Can you find the equation of the axis of symmetry from the given parabola?
5. How do you rewrite the factored form of a quadratic equation into standard form?

**Tip:** Always double-check the symmetry of a parabola by verifying that the vertex lies exactly between the x-intercepts.

This is the sketch of the graph of y = (x - 1)(x - 3). a) Write down the coordinates of points A and B. b) Write down the coordinates of point P. c) Write down the coordinates of the turning point Q.

Learn how to determine the coordinates of key points on the graph of y = (x - 1)(x - 3). This includes finding x-intercepts, the y-intercept, and the turning point of the parabola. Suitable for Grades 8-10.

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