Passes through (-3,7) and has vertex (-5,4)

y

=

−

3

x

2

+

30

x

−

71

Explanation:

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

here  

(

h

,

k

)

=

(

5

,

4

)

⇒

y

=

a

(

x

−

5

)

2

+

4

to find a substitute  

(

7

,

−

8

)

into the equation

−

8

=

4

a

+

4

⇒

a

=

−

3

⇒

y

=

−

3

(

x

−

5

)

2

+

4

←

in vertex form

distributing and simplifying gives

y

=

−

3

(

x

2

−

10

x

+

25

)

+

4

y

=

−

3

x

2

+

30

x

−

75

+

4

⇒

y

=

−

3

x

2

+

30

x

−

71

←

in standard form

Step-by-step explanation: