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Cerrena [4.2K]
2 years ago
13

Rewrite the given quadratic function in the form f(x) = a(x - h)2 + k. Then, enter the x-coordinate of the minimum point of the

function:
f(x)=4x^2-12x-15
Mathematics
1 answer:
klemol [59]2 years ago
6 0

Answer:

f(x)=4(x-\frac{3}{2})^2-24

The minimum occurs at x=\frac{3}{2}.

Step-by-step explanation:

f(x)=4x^2-12x-15

The a in f(x)=ax^2+bx+c is the same a in f(x)=a(x-h)^2+k where:

h=\frac{-b}{2a} and k=f(\frac{-b}{2a}).

So let's find \frac{-b}{2a}=\frac{-(-12)}{2(4)}=\frac{12}{8}=\frac{3}{2}.

f(\frac{-b}{2a})=f(\frac{3}{2}).

To find f(\frac{3}{2}), we must use the expression that f is and evaluate it for x=\frac{3}{2}, like so:

4(\frac{3}{2})^2-12(\frac{3}{2})-15

4(\frac{9}{4}-6(3)-15

9-18-15

-9-15

-24

So the vertex form is f(x)=4(x-\frac{3}{2})^2-24.

-----------------Another way----------------------------

You could just complete the square.

I like to use the following to help me formulate the process:

x^2+dx+(\frac{d}{2})^2=(x+\frac{d}{2})^2.

Let's start. My formula requires coefficient of x^2 to be 1 so factor out the 4 from the first two terms:

f(x)=4x^2-12x-15

f(x)=4(x^2-3x)-15

Now we are going to add the (\frac{d}{2})^2 to complete the square; whatever you add in you must also subtract out.

f(x)=4(x^2-3x+(\frac{3}{2})^2)-15-4(\frac{3}{2})^2

f(x)=4(x-\frac{3}{2})^2-15-4(\frac{9}{4})

f(x)=4(x-\frac{3}{2})^2-15-9

f(x)=4(x-\frac{3}{2})^2-24

-----------------So anyways either way you choose....-----------------------

The minimum or maximum will occur at the vertex. Since a is positive the parabola is open up and therefore does have a minimum.

f(x)=a(x-h)^2+k tells us the vertex is (h,k).

So h is the x-coordinate of the vertex.

So the minimum occurs at x=\frac{3}{2}.

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If a number’s composite form is 343, which of the following shows its exponential form as a product of prime numbers? A.7 · 49 B
Levart [38]

Answer:

a is the answer

Step-by-step explanation:

7×7×7=343

7×7=49

49×7=343

8 0
3 years ago
The exchange rate in some prehistoric village was 6 jagged rocks for every 2 smooth pebbles. Also, one shiny rock could be trade
Scrat [10]

30 Jagged rocks are the same 3 shiny rocks using the exchange rates provided(i.e. option D)

What is an exchange rate?

Exchange rate means the rate at which one item exchanges hands with another, for instance, in this case, 6 jagged rocks are equivalent to 2 smooth pebbles.

6 jagged rocks=2 smooth pebbles

divide both sides by 2

6/2 jagged rocks=2/2 smooth pebbles

3 jagged rocks=1 smooth pebble

We can rewrite as below:

1 jagged rock=1/3 smooth pebble

30jagged rocks=1/3*30 smooth pebbles

30 jagged rocks=10 smooth pebbles

Now we need to convert 10 smooth pebbles to shiny rock equivalence

3 smooth pebbles=1 shiny rock

1 smooth pebble=1/3 shiny rock

10 smooth pebbles=1/3*10 shiny rocks

10 smooth pebbles=3 shiny rocks( even though it is 3.33, but the final answer should be rounded to a whole number)

Read more about exchange rate in the link below:

brainly.com/question/2202418

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4 0
2 years ago
On a certain hot summer day, 673 people used the public swimming pool. The daily prices are 1.75 for children and 2.00 for adult
amid [387]

Answer:

Number of children = 386

Number of adults = 287

Step-by-step explanation:

Let

x = number of children

y = number of adults

x + y = 673 (1)

1.75x + 2y = 1249.50 (2)

From (1)

x = 673 - y

Substitute x = 673 - y into (2)

1.75x + 2y = 1249.50

1.75(673 - y) + 2y = 1249.50

1177.75 - 1.75y + 2y = 1249.50

- 1.75y + 2y = 1249.50 - 1177.75

0.25y = 71.75

y = 71.75/0.25

y = 287

Substitute y = 287 into (1)

x + y = 673

x + 287 = 673

x = 673 - 287

x = 386

Number of children = 386

Number of adults = 287

3 0
3 years ago
Given f(x) = 2x + 5 and g(x) = 3x + 6
Kryger [21]
I hope this helps you



f(8)=2.8+5=21


g(8)=3.8+6=30


f-g(8)=21-30= -9
6 0
3 years ago
Read 2 more answers
If 6 cubes with an edge length of 14 can fit the height of the prism, what is the height of the prism? Enter the missing part of
Paha777 [63]

Answer: 84\ \text{units}

Step-by-step explanation:

Given

The length of each cube is a=14\ \text{units}

If there are 6 cubes placed over each other, then the height achieved by the cubes is

\Rightarrow 6\times 14\\\Rightarrow 84\ \text{units}

7 0
2 years ago
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