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:

=====================================

explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer