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3 years ago

How to Find the vertex of f(x)=-8x^2-8x+7

Mathematics

1 answer:

charle [14.2K]3 years ago

7 0

Answer:

The answer to your question is: (1/2, 5)

Step-by-step explanation:

Parabola f(x) = 8x² - 8x + 7

y = 8x² - 8x + 7

Vertical Parabola equation

( x - h)² = 4p (y - k) Transform the original equation to this form

8x² - 8x = y - 7

8(x² - x + ( )²) = y - 7 Complete squares

8 (x² - x + (1/2)²) = y - 7 + 2 Simplification

8 (x² - x + 1/4) = y - 5

(x - 1/2)² = 1/8 (y - 5)

Finally Vertex

(1/2 , 5)

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musickatia [10]

Assume that the initial coordinates are (x,y) and that the dilated coordinates are (x',y').

The dilation is therefore:
(x,y) ............> (x',y')

Now, let's assume that the dilation factor is k.
Therefore:
x' = kx
y' = ky

Based on the above, all the student has to do is get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k.

Example:
Assume an original point at (2,4) is dilated to coordinates (4,8). Find the dilation factor.
Assume the dilation coefficient is k.
(x,y) are (2,4) and (x',y') are (4,8)
Therefore:
x' = kx .........> 4 = k*2 ..........> k = 2
or:
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Based on the above, the dilation coefficient would be 2.

Hope this helps :)

8 0

3 years ago

Read 2 more answers

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alex41 [277]

Answer:

The answers are given in the attachment

Step-by-step explanation:

The detailed step by step calculations are shown in the attachment.

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3 years ago

Courtney works at the local shoe store and receives $150 a week plus 3% of all sales over $1000. This week her sales were $3200.

schepotkina [342]

The equation you would use to find her earning for the week would be:

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3 years ago

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. what is the approximate area

aniked [119]

The area of the regular heptagon which has a radius of approximately 27.87 cm and the length of each side is 24.18 cm is 2125 cm².

<h3>What is the area of a heptagon?</h3>

Heptagon is the closed shape polygon which has 7 sides and 7 interior angles.

The area of the regular heptagon is found out using the following formula.

$A=\dfrac{7a}{4}\cot \left(\dfrac{180}{7}\right)$

Here, (<em>a</em>) is the length of the heptagon.

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. Put the value of side in the above formula,

$A=\dfrac{7\times24.18}{4}\cot \left(\dfrac{180}{7}\right)\\A\approx 2125\rm\; cm^2$

Hence, the area of the regular heptagon which has a radius of approximately 27.87 cm and the length of each side is 24.18 cm is 2125 cm².

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2 years ago

Find the value of Y

Anna35 [415]

Answer:

y=19

Step-by-step explanation:

2y + 2 = 180 - 120 -20

2y = 40 - 2

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3 years ago