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Worked Example 3: Quadratic Equation

Solve graphically: x² - 2x - 3 = 0

Step 1 Set up parabola equation

y = x² - 2x - 3

This is a U-shaped parabola (a > 0)

Step 2 Find key points

y-intercept: (0, -3)

Vertex: x = -b/2a = -(-2)/2(1) = 1

At x = 1: y = 1 - 2 - 3 = -4

Vertex: (1, -4)

Step 3 Plot and find x-intercepts

Parabola crosses x-axis at two points

Reading from graph: x = -1 and x = 3

Solutions: x = -1 or x = 3

Step 4 Verify solutions

x = -1: (-1)² - 2(-1) - 3 = 1 + 2 - 3 = 0 ✓

x = 3: (3)² - 2(3) - 3 = 9 - 6 - 3 = 0 ✓

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