1 quadratic formula. y 2 quadratic formula: geometric interpretation solve x 0

1

Quadratic formula

𝑥=−𝑏±√𝑏2−4𝑎𝑐2𝑎

𝑎𝑥2+𝑏𝑥+𝑐=0Solve

y

2

Quadratic formula: Geometric interpretation

𝑦𝑄𝑈𝐴𝐷 (𝑥 )=𝑎𝑥2+𝑏𝑥+𝑐

Solve

x

𝑎𝑥2+𝑏𝑥+𝑐=0

0

y

3



Solve 𝑎𝑥2+𝑏𝑥+𝑐=0

0x

y


4



0x

y


5



0x

y


6



0x

y


7



0x

x

y

8


Solve

𝑦 𝑍𝐸𝑅𝑂 (𝑥 )=0

𝑎𝑥2+𝑏𝑥+𝑐=0


0

9

Quadratic formula: Analytic solution


𝑥2+𝑏𝑎𝑥+

𝑐𝑎

=0𝑎=0

𝑥2+𝑏𝑎𝑥+( 𝑏2𝑎)

2

−( 𝑏2𝑎 )2

+𝑐𝑎

=0

𝑥2+𝑏𝑎𝑥+

𝑐𝑎

=0𝑎=0

10



2

−( 𝑏2𝑎 )2

+𝑐𝑎

=0

STOP Check this step: Expand (x + b/2a)2(𝑥+ 𝑏

2𝑎 )2

−[√( 𝑏2𝑎 )2

−𝑐𝑎 ]

2

=0


11


2

−( 𝑏2𝑎 )2

+𝑐𝑎

=0

(𝑥+ 𝑏2𝑎 )

2

−[√( 𝑏2𝑎 )2

−𝑐𝑎 ]

2

=0

[(𝑥+𝑏

2𝑎 )−√( 𝑏2𝑎 )2

−𝑐𝑎 ] [(𝑥+

𝑏2𝑎 )+√( 𝑏2𝑎 )

2

−𝑐𝑎 ]=0

(𝑥+ 𝑏2𝑎 )∓√( 𝑏2𝑎 )

2

−𝑐𝑎

=0

𝑥=− 𝑏2𝑎±√( 𝑏2𝑎 )

2

−𝑐𝑎

𝑥=−𝑏±√𝑏2−4𝑎𝑐2𝑎

𝑥2+𝑏𝑎𝑥+

𝑐𝑎

=0𝑎=0



1 quadratic formula. y 2 quadratic formula: geometric interpretation solve x 0

Documents