The question involves solving mathematical problems related to the graph of $y = x^2 + 2x - 3$, and it appears to require graph plotting, solving for roots, and determining the axis of symmetry and minimum point.

Summary of the tasks:

1. (b) Draw the graph of $y = x^2 + 2x - 3$ for $-4 \leq x \leq 2$ using the table provided (scale: 2 cm to 1 unit on both axes).
2. (c) Analyze the graph:
   • (i) Solve $y = x^2 + 2x - 3$ for roots.
   • (ii) Determine the axis of symmetry and minimum point when the graph reflects on the y-axis.

Explanation and Steps:

(b) Graph plotting:

Using the given table:

• Plot the points $(-4, 5), (-3.5, 2.25), (-3, 0), (-2, -3), (-0.5, -3.75), (0.5, -1.75), (2, 5)$.
• Connect these points to form the parabola.

(c) Analysis:

1. (i) Solve $y = 0$ for $y = x^2 + 2x - 3$:

   • Factorize $x^2 + 2x - 3 = 0$.
   • Roots: $(x + 3)(x - 1) = 0$, giving $x = -3$ and $x = 1$.

2. (ii) Determine the axis of symmetry and minimum point:

   • Equation of axis of symmetry is $x = -\frac{b}{2a}$.
     • For $y = x^2 + 2x - 3$, $a = 1, b = 2$: $x = -\frac{2}{2(1)} = -1$.
   • Minimum point:
     • Substitute $x = -1$ into $y = x^2 + 2x - 3$: $y = (-1)^2 + 2(-1) - 3 = -4$.
     • Minimum point: $(-1, -4)$.

Would you like more details on any specific step or guidance with graph drawing?

Related Questions:

1. How do you derive the roots of quadratic equations by completing the square?
2. What are the general steps to find the vertex of a parabola?
3. Why is the axis of symmetry always given by $x = -\frac{b}{2a}$?
4. What does reflecting a graph on the y-axis entail?
5. How does the discriminant of a quadratic equation relate to the graph?

Tip:

When graphing, ensure your scale is consistent to accurately represent the points and symmetry of the parabola.