Families of Quadratic Polynomial Functions (VCE SSCE Mathematical Methods): Flashcards

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Families of Quadratic Polynomial Functions
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Family of parabolas definition

Group of quadratic functions sharing common characteristics

Parameters in quadratic families

Letters (aa, bb, hh, kk) representing variable values

Effect when a>0a > 0

Parabola opens upward

Effect when a<0a < 0

Parabola opens downward

Effect of larger a|a| on parabola

Makes parabola narrower

When to use intercept form y=a(xe)(xf)y = a(x - e)(x - f)

When you know two xx-axis intercepts

When to use turning point form y=a(xh)2+ky = a(x - h)^2 + k

When you know the turning point coordinates

When to use general form y=ax2+bx+cy = ax^2 + bx + c

When you know three points on the parabola

Discriminant value when parabola touches xx-axis once

Δ=0\Delta = 0

(h,k)(h, k) in turning point form

Coordinates of the turning point

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