Standard, factored and vertex form

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Learn it Standard form $y = ax^2 + bx + c$ shows the y-intercept c. Factored form $y = a(x - r)(x - s)$ shows the zeros r and s. Vertex form $y = a(x - h)^2 + k$ shows the vertex (h, k). If a > 0 it opens up; if a < 0 it opens down.

Example: $y = 2(x - 1)(x - 5)$

Zeros: x = 1 and x = 5.
Axis of symmetry: halfway, x = 3.
Vertex y: $2(3 - 1)(3 - 5) = -8$. Minimum at (3, −8).

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