Where y = x² - 2x - 3 meets the x-axis

For the parabola y = x² - 2x - 3, find the coordinates of its intersections with the x-axis.

Step-by-step

1. Δ = b² − 4ac = (-2)² − 4×1×-3 = 16
   Compute the discriminant first to count the real roots
2. x = (2 ± √16) ÷ 2
   Substitute into the quadratic formula
3. x₁ = 3, x₂ = -1
   Give both real roots

Why it works

Where a parabola meets the x-axis the y-coordinate is 0, so setting y = 0 turns the question into solving a quadratic equation for the x-coordinates.

Common mistakes

• Answering with the y-intercept (0, -3).
• Losing the negative root and giving only x = 3.

Related

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