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rjkz [21]
3 years ago
15

How can you use the values of a, b, and c to write a quadratic function in vertex form?

Mathematics
1 answer:
olga_2 [115]3 years ago
3 0

Answer:

  y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)

Step-by-step explanation:

We presume you're starting with ...

  y = ax^2 +bx +c

As you would with numbers, factor the first two terms:

  y = a(x^2 +b/a·x) +c

Add half the square of the x term inside and its opposite outside parentheses:

  y = a(x^2 +(b/a)x + (b/(2a))^2) + c - a(b/(2a))^2

  y = a(x +b/(2a))^2 +c -b^2/(4a)

You can combine the last two terms to a more familiar fraction:

  y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)

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The Jones family had two gallons of milk before breakfast. The family used two quarts of milk during breakfast. How many quarts
mixer [17]

Answer:

2

Step-by-step explanation:

3 0
2 years ago
A box is to be made where the material for the sides and the lid cost​ $0.20 per square foot and the cost for the bottom is ​$0.
Reika [66]

Answer:

The dimension of the box is l×w×h =  (2.274 × 2.274 × 1.934) ft³

Step-by-step explanation:

From the given information;

Let a be the cost of the box

Let b  be one side of the square base ;    &

h to be the height  of the box

We know that the volume of the box = 10 cubic feet

Then;

a²h = 10

h = 10/a²

The base = (0.65)a²

The top = (0.2)a²

The side = (0.2) a × 25/a²

= 5/a

For the four sides of the box now ;

= (0.2) 4a × 25/a²

= 0.8  × 25/a

= 20 /a

The total cost of the box is:

b = 0.65a² + 0.2a² + 20 /a

b = 0.85 a² + 20 /a

Taking differential of b with respect to a ;we have:

db/da = 1.7a - 1/a²(20) = 0

1.7 a³ - 20 = 0

1.7 a³  = 20

a³ = 20/1.7

a³ = 11.77

a = \sqrt[3]{11.77}

a = 2.274 ft

Thus; the cost for the base of the box = (0.65)a²

the cost for the base of the box =(0.65) × ( 2.274)²

the cost for the base of the box = 3.362

The top of the box = (0.2)a²

The top of the box = (0.2)× ( 2.274)²

The top of the box = 1.034

The four sides of the box = 20 /a

The four sides of the box = 20/2.274

The four sides of the box = 8.795

the total cost = b = 0.85 a² + 20 /a

the total cost = 0.85 (2.274)² + 20 /2.274

the total cost = 4.395 + 8.795

the total cost = 13.19

Recall that:

the volume of the box = 10 cubic feet

Then;

a²h = 10

h = 10/a²

h = 10/ 2.274²

h  1.934

The dimension of the box is l×w×h =  (2.274 × 2.274 × 1.934) ft³

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3 years ago
Can you help me with this question please
vaieri [72.5K]
To get the answer, divide 55 by 610. the answer would be 11.09 i’m pretty sure
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