Mathematics — first biennium · Lesson
The zeros of y=ax²+bx+c are the x-coordinates where the parabola meets the x-axis. With two distinct zeros, the symmetry axis lies halfway between them.
Prerequisites: Parabola transformations and factorization
Goal: Connect general form, symmetry axis, intercept and zeros of a quadratic function.
In this lesson: Connect general form, symmetry axis, intercept and zeros of a quadratic function.
New concept: The zeros of a function are the x-values for which y=0: on the graph they are the x-intercepts. For a parabola, the axis of symmetry passes through the vertex and, when there are two zeros, lies halfway between them.
How to proceed: Factor to check the zeros; their average must match −b/(2a).
You can already assume: Parabola transformations and factorization.
Vary a, b and c to observe changes in concavity, vertex position and axis intersections.
With a = 0 the curve loses this family's characteristic shape; also try a non-zero value.
The highlighted zeros are exactly the solutions of f(x)=0.
Completed exercises: 0/5 · Correct on first attempt: 0
Factor to check the zeros; their average must match −b/(2a).
Data / situation: y=x²−6x
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