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fR
f(x) = ax2+bx +c
a b c a
a b c
c f(0) =
c

f(x) = ax2+bx +c x
f
f(x) = a(x−α)2+β
α=−
b
2aβ=f(α)
β=f(α)f
a a
(α,β)
f
β x =α
x
f(x) = −8x2−32x−39
fRf(x) = −2(x+1)2−2

f(x) = ax2+bx +c x
f
f(x) = a(x−x1) (x−x2)
x1x2
x1x2
f(x1) = f(x2)=0 f
f f(x) =
0
x1x2
x
y=f(x)
x1x2
x2+ 1
−2(x−1)(x+ 3) 1 −3
f(x)
f(x)=0

f(x) = x2−4
g(x) = x2−2x+ 1
f(x) =
x2+ 2√2x−6
f(x) = −3(x−1)2+ 12
f(x) = 0
−3(x−1)2+ 12 = 0
−3(x−1)2+ 12 = 0
−3(x−1)2=
−3(x−1)2
=
(x−1)2=
p(x−1)2=√
x−1 =
x−1 =
x=
p(x−1)2=−√
x−1 =
x−1 =
x=
f(x) = 2(x+3)2+8 f(x) = 0
2(x+ 3)2+ 8 = 0
2(x+ 3)2+ 8 = 0
2(x+ 3)2=

f(x) = ax2+bx +c
f(x) = ax−−b
2a2
−
b2 −4ac
4a
x−−b
2a2
=b2
−4ac
4a2
b2 −4ac
∆
∆ = b2 −4ac
x1=−b−√∆
2ax2=−b+√∆ 2a
−3x2−6x+ 24 = 0
2x2+ 24x+ 72 = 0
x2+x+ 1 = 0