The graph of y = ax² + bx + c is a U-shaped curve called a parabola. If a is negative, it is upside down. The curve crosses the y-axis at (0, c) and crosses the x-axis at the roots, where y = 0.
To find the roots, solve the equation ax² + bx + c = 0. The turning point lies halfway between the roots, on the line of symmetry. For y = x² − 5x + 6 = (x − 2)(x − 3), the roots are 2 and 3, the y-intercept is (0, 6) and the line of symmetry is x = 2.5.
Worked example
Find the roots of y = (x + 5)(x − 1).
- Roots are where y = 0.
- x + 5 = 0 or x − 1 = 0.
Answer:x = −5 and x = 1
Key words
- parabola
- the curve of a quadratic
- root
- where the curve crosses the x-axis
- line of symmetry
- the vertical line through the turning point
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Common Core-referenced: HSF-IF.C.7a