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Where y = x² - 5x + 6 meets the x-axis
For the parabola y = x² - 5x + 6, find the coordinates of its intersections with the x-axis.
Answer
x₁ = 3, x₂ = 2
Step-by-step
- Δ = b² − 4ac = (-5)² − 4×1×6 = 1Compute the discriminant first to count the real roots
- x = (5 ± √1) ÷ 2Substitute into the quadratic formula
- x₁ = 3, x₂ = 2Give 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, 6).
- Giving only the two x-values 2 and 3 instead of the points (2, 0) and (3, 0).