2 degree polynomial , quadratic

A quadratic (better to say 2 degree polynomial) has a leading term of $a{x}^2$.

A quadratic can be in standard form, turning point form or product form.

The graph of a quadratic is called a parabola. The graph has:

• either a positive or negative shape
• one y-intercept
• x-intercepts, also called roots
• a turning point a point on the graph, either the maximum or minimum
• an axis of symmetry that includes the turning point
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standard form

$f(x)=a{x}^2+bx+c$

• the sign of $a$ determines the shape
• the axis of symmetry is $x=\frac{-b}{2a}$
• find the x-intercepts with $y=0$
• find the turning point with axis of symmetry or with x-intercepts

turning point form

$f(x)=a(x-h{)}^2+k$

• the sign of $a$ determines the shape
• $(h,k)$ is the turning point
• the y intercept is at $(0,a{h}^2+k)$
• find the x-intercepts by substituting $y=0$

product form

$f(x)=a(x-m)(x-n)$

• the sign of $a$ determines the shape
• where a and b are constants
• x-intercepts are are $(m,0)$ and $(n,0)$