Question

Rewrite the function y = x^2 - 6x + 14 in vertex form, y = (x - h)^2 + k.

Answer 1

Answer: y = (x - 3)² + 5

Step-by-step explanation:

  y   = x² - 6x + 14

  -14               -14

y - 14 = x² - 6x

y - 14 +  9   = x² - 6x +  9  

             ↑            ↓       ↑

                         $\frac{-6}{2}$ = (-3)²

y - 5 = (x - 3)²

  +5              +5

y      = (x - 3)² + 5

Answer 2

the equation of a parabola in

vertex form

is.

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∣

∣

∣

2

2

y

=

a

(

x

−

h

)

2

+

k

2

2

∣

∣

∣

−−−−−−−−−−−−−−−−−−−−−

where

(

h

,

k

)

are the coordinates of the vertex and a

is a multiplier

to obtain this form

complete the square

y

=

x

2

+

2

(

4

)

x

+

16

−

16

+

14

⇒

y

=

(

x

+

4

)

2

−

2

←

in vertex form

⇒

vertex

=

(

−

4

,

−

2

)

to obtain the intercepts

∙

let x = 0, in the equation for y-intercept

∙

let y = 0, in the equation for x-intercept

x

=

0

⇒

y

=

0

+

0

+

14

=

14

←

y-intercept

y

=

0

⇒

(

x

+

4

)

2

−

2

=

0

←

add 2 to both sides

⇒

(

x

+

4

)

2

=

2

take the square root of both sides

√

(

x

+

4

)

2

=

±

√

2

←

note plus or minus

⇒

x

+

4

=

±

√

2

←

subtract 4 from both sides

⇒

x

=

−

4

±

√

2

←

exact values

graph{(y-x^2-8x-14)((x+4)^2+(y+2)^2-0.04)=0 [-10, 10, -5, 5]}