Equations of Parabolas (HSC SSCE Mathematics Advanced): Flashcards

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Equations of Parabolas
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Standard form of quadratic

f(x)=ax2+bx+cf(x) = ax^2 + bx + c

Vertex form of quadratic

f(x)=a(xh)2+kf(x) = a(x - h)^2 + k

Factorised form of quadratic

f(x)=a(xx1)(xx2)f(x) = a(x - x_1)(x - x_2)

In std form ax2+bx+cax^2+bx+c, cc represents

y-intercept

In vertex form a(xh)2+ka(x-h)^2+k, point (h,k)(h,k) is

The vertex

In factorised form, x1x_1 & x2x_2 are

x-intercepts (roots or zeros)

If a>0a > 0, parabola is

Concave up (opens upward)

Domain of any parabola

All real numbers (R\mathbb{R})

Use vertex form when you know

Vertex and one other point

Use factorised form when you know

x-intercepts and one other point

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