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melomori [17]
3 years ago
14

What is the vertex form of the parabola whose standard form equation is y=5x^2-30x+49

Mathematics
1 answer:
agasfer [191]3 years ago
7 0

Answer:

The vertex is (3,4)

Step-by-step explanation:

To convert a quadratic from  

y = a x 2 + b x + c

form to vertex form,

y = a ( x − h ) 2 + k , you use the process of completing the square.

First, we must isolate the  x

terms:

y − 49 = 5 x 2 − 30 x + 49 − 49

y − 49 = 5 x 2 − 30 x

We need a leading coefficient of  1

for completing the square, so factor out the current leading coefficient of 2.

y − 49 = 5 ( x 2 − 6 x )

Next, we need to add the correct number to both sides of the equation to create a perfect square. However, because the number will be placed inside the parenthesis on the right side we must factor it by  

2

on the left side of the equation. This is the coefficient we factored out in the previous step.

y − 49 + ( 5 ⋅ ? ) = 5 ( x 2 − 6 x + ? )

<- Hint:  

62 = 3 ;  3 ⋅ 3 = 9

y − 49 + ( 5 ⋅ 9 ) = 5 ( x 2 − 6 x + 9 )  

y− 49 + 45 = 5 ( x 2 − 6 x + 9 )

y − 4 = 5 ( x 2 − 6 x + 9 )

Then, we need to create the square on the right hand side of the equation:

y − 4 = 5 ( x − 3 ) 2

Now, isolate the  y  term:

y − 4 + 4 = 5 ( x − 3 ) 2 + 4

y − 0 = 5 ( x − 3 ) 2 + 4

y − 0 = 5 ( x − 3 ) 2 + 4

The vertex is:  

( 3 , 4 )

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How much does 1 1/4 pounds of turkey that cost $2.85 per pound cost
lidiya [134]
Answer: $3.56, since one pound is $2.85, 1/4 is .25 (as a decimal). Then .25x2.85=$0.71+$2.85=$3.56
I hope this helped!
4 0
3 years ago
The units of the subway map below are in miles. Suppose the routes between
levacccp [35]

Distance between Station E  and Station G  is 8.48 miles (Approx.)

<u>Given:</u>

Distance 3 miles east

Distance 5 miles south

<u>Find:</u>

Distance between Station E  and Station G

<u>Computation:</u>

Co-ordinate of Point E = (-3 , 1)

Co-ordinate of Point G is 3 mile east and 5 mile south

So,

Co-ordinate of Point G = (3 , -5)

Distance between two point = √(x2 - x1)² + (y2 - y1)²

So,

Distance between Station E  and Station G  = √(3 + 3)² + (-5 - 1)²

Distance between Station E  and Station G  = √(6)² + (-6)²

Distance between Station E  and Station G  = √36 + 36

Distance between Station E  and Station G  = √72

Distance between Station E  and Station G  = 8.48 miles (Approx.)

Learn more:

brainly.com/question/12052812?referrer=searchResults

4 0
2 years ago
Can anybody help me please
klio [65]

Answer:

x    y

0   -1

-1    0

-8    7

Step-by-step explanation:

y = -x - 1

when x = 0, y = -1

when y = 0

0 = -x - 1

x = -1

when x = -8,

y = -(-8) - 1

y = 7

8 0
3 years ago
Read 2 more answers
Does this graph have any vertical asymptotes? If so, where?
tresset_1 [31]

Answer:

There are no vertical asympotes for this rational function.

Step-by-step explanation:

For rational functions, a vertical asymptote exists for every value of the independent variable such that function become undefined, that is, such that denominator is zero. Let be the following rational function:

C(p) = \frac{25000\cdot p}{100-p}, 0\le p < 100

There is a vertical asymptote for this case:

100-p = 0

p = 100

Which is out of the interval given to the rational function. Hence, we conclude that there are no vertical asympotes for this rational function.

5 0
2 years ago
Luke has $21 more than rachel and $48 more than daniel. altogether they have $168. how much does luke have?
Anettt [7]

this can be solve by 3 variable equation

let x be the money of luke

y money of rachel

z money of daniel

first equation

x = y + 21

second equation

x = z + 48

third equation

x + y + z = 168

solving simultaneously

x =79

y = 58

z = 31

<span> </span>

7 0
3 years ago
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