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

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

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

id: 1741511532220
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A quadratic in standard form is $f(x)=ax^2+bx+c$. The axis of symmetry is ==$x=\dfrac{-b}{2a}$==.

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 $y = 0$

id: 1741511533020
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A quadratic in turning point form is ==$f(x)=a(x-h)^2+k$==. The turning point

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 $(n, 0)$