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kotegsom [21]
3 years ago
12

How is the graph of y = (x + 1)^2- 5 transformed from the graph of y=x^2?

Mathematics
1 answer:
Ainat [17]3 years ago
8 0

\text{Hi there! :D}

\boxed{\text{There is a horizontal shift of 1 unit left and 5 units down.}}

\text{Recall that the transformations form of a quadratic function is:}\\\\y = \pm a(b(x-h))+k \text{ where:}\\\\a = \text{ vertical stretch/compression}\\\\b = \text{ horizontal stretch/compression}\\\\h = \text{ shift left/right}\\\\k = \text{ shift up/down}\\\\\text{Therefore, in this instance:}\\\\h = -1\\\\k = -5, \text{ so:}\\\\\text{There is a horizontal shift of 1 unit left and 5 units down.}

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Find the center and radius of the circle (x+3)^2+(y-1)^2=81
sasho [114]

The equation of a circle is written as ( x-h)^2 + (y-k)^2 = r^2

h and k is the center point of the circle and r is the radius.

In the given equation (x+3)^2 + (y-1)^2 = 81

h = -3

k = 1

r^2 = 81

Take the square root of both sides:

r = 9

The center is (-3,1) and the radius is 9

5 0
3 years ago
Need help badly plssssss
Ksenya-84 [330]

Answer:

translation then reflection

Step-by-step explanation:

6 0
3 years ago
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The difference of the square of a number and 28 is equal to 3 times that number
Pepsi [2]

Answer:

- 4, 7

Step-by-step explanation:

Let the required number be x.

Therefore, according to the given condition:

{x}^{2}  - 28 = 3x \\  {x}^{2}  - 3x - 28 = 0 \\  {x}^{2}  - 7x + 4x - 28 = 0 \\ x(x - 7) + 4(x - 7) = 0 \\ (x - 7)(x + 4) = 0 \\ x - 7 = 0 \: or \: x + 4 = 0 \\ x = 7 \: or \: x =  - 4 \\

5 0
3 years ago
Please help me .
Margarita [4]

Answer:

(2x + 3)(x - 2)

Step-by-step explanation:

use FOIL

First, Outside, Inside, Last

2x x x = 2x²

2x x -2 = -4x

3 x x = 3x

3 x -2 = -6

2x² - 4x + 3x - 6

5 0
2 years ago
I need help!! Find the area of each shaded segment. Round your answer to the nearest 10th
guajiro [1.7K]

Given:

θ = 60°

Radius = 8 in

To find:

The area of the shaded segment.

Solution:

Vertically opposite angles are congruent.

Angle for the shaded segment = 60°

<u>Area of the sector:</u>

$A=\pi r^2\times \frac{\theta}{360^\circ}

$A=3.14 \times 8^2\times \frac{60^\circ}{360^\circ}

A = 33.5 in²

Area of the sector = 33.5 in²

<u>Area of triangle:</u>

$A=\frac{1}{2} bh

$A=\frac{1}{2} \times 8\times 8

A = 32 in²

Area of the triangle = 32 in²

Area of segment = Area of sector - Area of triangle

                            = 33.5 in² - 32 in²

                            = 1.5 in²

The area of the shaded segment is 1.5 square inches.

8 0
3 years ago
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