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marin [14]
3 years ago
15

Graph the function using its vertex, axis of symmetry, and intercepts. f (x) = x2 – 12x + 36

Mathematics
1 answer:
slamgirl [31]3 years ago
6 0

Answer:

To graph a quadratic equation we first need to factorise it into a different form.

First we check what the discriminant is equal to

Where

f

(

x

)

=

a

x

2

+

b

x

2

+

c

Δ

(Discriminant)

=

b

2

−

4

a

c

In this case

Δ

=

3

2

−

4

⋅

2

⋅

7

Δ

=

−

47

Because it is less than zero it can't be factored normally

Therefore we must use the The Quadratic Formula or Completing the Square

Here I have completed the square

f

(

x

)

=

2

x

2

−

3

x

+

7

Remove factor from

x

2

term

f

(

x

)

=

2

⋅

(

x

2

−

3

2

x

+

7

2

)

Take

x

term, half it and then square it

f

(

x

)

=

−

3

2

→

−

3

4

→

9

16

Add and then subtract this number inside the equation

f

(

x

)

=

2

⋅

(

x

2

−

3

2

x

+

9

16

−

9

16

+

7

2

)

Combine the first three terms in a perfect square

f

(

x

)

=

2

⋅

(

(

x

−

3

4

)

2

−

9

16

+

7

2

)

Equate left over terms

f

(

x

)

=

2

⋅

(

(

x

−

3

4

)

2

+

47

16

)

Multiply coefficient back in

f

(

x

)

=

2

(

x

−

3

4

)

2

+

47

8

This gives a turning point of

(

3

4

,

47

8

)

=

(

0.75

,

5.875

)

and a

y

intercept of

2

⋅

(

3

4

)

2

+

47

8

=

(

0

,

7

)

enter image source here

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7,051,004,264 in expanded notation
riadik2000 [5.3K]

7,000,000,000 + 0 + 50,000,000 + 1,000,000 + 0 + 0 + 4,000 + 200 + 60 + 4

I’m not sure if you’re supposed to put the commas in it

3 0
3 years ago
in a canoe race, a team paddles downstream 480 m in 60 s. The same team makes the trip upstream in 80 s. Find the team's rate in
Vera_Pavlovna [14]
480=60(v+s) 

480=60v+60s

8=v+s

s=8-v...

480=80(v-s)  using s from above we get:

480=80(v-(8-v))

6=v-8+v

6=2v-8

2v=14

v=7, and since s=8-v, s=1

So the rate of the team is 7m/s while the rate of the stream is 1m/s





7 0
3 years ago
A 10-foot by 12-foot wall has two windows that measure 3 feet by 5 feet each.
musickatia [10]

12 ft maybe? i dunno im sorry if this is wrong

6 0
3 years ago
79% of 67 miles is what?
KIM [24]
To do it without a calculator:

10% of 67 is 6.7
6.7 x 8 is 53.6 (80%)
1% of 67 is .67
<span>53.6 - .67 is 52.93 (79%)</span>
3 0
3 years ago
Read 2 more answers
14.
hoa [83]
D
You subtract 5 1/4 (5.25) - 3 3/4 (3.75) = 1 1/2 (1.5)
3 0
3 years ago
Read 2 more answers
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