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Valentin [98]
4 years ago
15

Given ​ f(x)=x^2−2x−5​. Enter the quadratic function in vertex form.

Mathematics
1 answer:
FrozenT [24]4 years ago
8 0

Answer:

f(x) = (x-1)^2-6

Step-by-step explanation:

Rewrite the quadratic using the method of completing the square:

x^2-2x-5=(x^2-2x+1)-1-5=(x-1)^2-6\\f(x) = (x-1)^2-6

From this form it is immediately clear that the vertex of the parabola is at x=1 and its y-intercept at -6.

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Layana’s house is located at (2 and two-thirds, 7 and one-third) on a map. The store where she works is located at (–1 and one-t
NeTakaya

We have been given that Layana’s house is located at (2\frac{2}{3}, 7\frac{1}{3}) on a map. The store where she works is located at (-1\frac{1}{3}, 7\frac{1}{3}).

We are asked to find the distance from Layana’s home to the store

We will use distance formula to solve our given problem.

Let us convert our given coordinates in improper fractions.

2\frac{2}{3}\Rightarrow \frac{8}{3}

7\frac{1}{3}\Rightarrow \frac{22}{3}

-1\frac{1}{3}\Rightarrow -\frac{4}{3}

Now we will use distance formula to solve our given problem.

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Upon substituting coordinates of our given point in above formula, we will get:

D=\sqrt{(\frac{22}{3}-\frac{22}{3})^2+(\frac{8}{3}-(-\frac{4}{3}))^2}

D=\sqrt{(0)^2+(\frac{8}{3}+\frac{4}{3})^2}

D=\sqrt{0+(\frac{8+4}{3})^2}

D=\sqrt{(\frac{12}{3})^2}

D=\sqrt{(4)^2}

D=4

Therefore, the distance from Layana's home to the store is 4 units and option A is the correct choice.

3 0
3 years ago
Read 2 more answers
In order to clear out room for new merchandise, James decided to mark down some of the items for sale in his electronics store.
sergiy2304 [10]

Answer:

a) Which item’s price was reduced by more, and by how many dollars more was it reduced?

The DVD player's price was reduced more by $3.82 than the stereo tuner's price.

b) Round all dollar values to the nearest cent.

Rounding $3.82 dollars to the nearest cents

$1 = 100 cents

$3.82 =

3.82 × 100 cents

= 382 cents

The DVD player's price was reduced by 382 cents more than the stereo tuner's price

Step-by-step explanation:

Lets day the original price of the DVD player was $100

We are told the price was marked down to 36%

36% of $100 = $36

$100 - $36 = $64

We are told the DVD cost $41.60 after the markdown.

Original cost of DVD =

$41.60/$64 × 100 = $65

Lets the original price of the Stereo player was $100

We are told the price was marked down to 22%

22% of $100 = $22

$100 - $22 = $78

We are told the DVD cost $69.42 after the markdown.

Original cost of Stereo =

$69.42/$78 × 100 = $89

DVD = $65 - $41.60 = $23.40 less 

Stereo = $89 - 69.42 = $19.58 less

Difference between the DVD and the Stereo is

$23.40 - $19.58 = $3.82

Therefore,the DVD player's price was reduced by $3.82 more than the stereo tuner's price

Rounding $3.82 dollars to the nearest cents

$1 = 100 cents

$3.82 =

3.82 × 100 cents

= 382 cents

8 0
3 years ago
Read 2 more answers
The width of a rectangle is 3 yards less than its length. The perimeter is 130 yards. Find the length and width of the rectangle
topjm [15]

Answer: length = 62 yards and width = 3 yards

Step-by-step explanation:

3 0
3 years ago
Which decimal is less than 2.87? 2.859 C. 2.971 b. 2.8711 d. 2.88 Please select the best answer from the choices provided ​
castortr0y [4]

Answer:

Step-by-step explanation:

2.859 is less than the rest

4 0
3 years ago
Please help im giving 95 points
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A. How many amoebas are there after 1 hour
8 0
3 years ago
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