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2 years ago

What does the quadratic function

Mathematics

1 answer:

nikklg [1K]2 years ago

6 0

Answer:

f(x) = (x -3)^2 - 1

Step-by-step explanation:

f(x) = x^2 - 6x + 8

a = 1, b = -6 and c = 8

So we are finding half of the b equation (ignore the negative sign)

Half of 6 is 3, so we are going to square 3 (3^2 = 9) and add 9 to the left side and subtract 9 to the right side

(x) = (x^2 - 6x + 9) + (8 - 9)

You can tell the polynomial is a perfect square, so we will have to factor it using the perfect square method

(x^2 - 6x + 9)

square toot of x^2 is x and square root of 9 is 3 and the operation sign after the a number is a minus sign

(x -3)^2

Don't forget the rest of the equation from before

(x -3)^2 + (8 - 9)

(x -3)^2 - 1

So the equation is f(x) = (x -3)^2 - 1

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Right triangle ABC and its image, triangle A'B'C' are shown in the image attached.

AlladinOne [14]

Answer:

See explanation

Step-by-step explanation:

Triangle ABC ha vertices at: A(-3,6), B(0,-4) and (2,6).

Let us apply 90 degrees clockwise about the origin twice to obtain 180 degrees clockwise rotation.

We apply the 90 degrees clockwise rotation rule.

$(x,y)\to (y,-x)$

$\implies A(-3,6)\to (6,3)$

$\implies B(0,4)\to (4,0)$

$\implies C(2,6)\to (6,-2)$

We apply the 90 degrees clockwise rotation rule again on the resulting points:

$\implies (6,3)\to A''(3,-6)$

$\implies (4,0)\to B''(0,-4)$

$\implies (6,-2)\to C''(-2,-6)$

Let us now apply 90 degrees counterclockwise rotation about the origin twice to obtain 180 degrees counterclockwise rotation.

We apply the 90 degrees counterclockwise rotation rule.

$(x,y)\to (-y,x)$

$\implies A(-3,6)\to (-6,-3)$

$\implies B(0,4)\to (-4,0)$

$\implies C(2,6)\to (-6,2)$

We apply the 90 degrees counterclockwise rotation rule again on the resulting points:

$\implies (-6,-3)\to A''(3,-6)$

$\implies (-4,0)\to B''(0,-4)$

$\implies (-6,2)\to C''(-2,-6)$

We can see that A''(3,-6), B''(0,-4) and C''(-2,-6) is the same for both the 180 degrees clockwise and counterclockwise rotations.

7 0

2 years ago

The letters of ALABAMA and LAMB were placed on separate slips of paper and put into two different bags.

labwork [276]

Answer:

45%

Step-by-step explanation:

There are 5 A's out of a total of 11 letters which is 5/11. 5/11 as a decimal is 0.45 which, as a percentage, is 45%

5 0

2 years ago

Elaina just began working as an occupational therapist assistant for $21.00 per hour. For each paycheck she receives, 12% is ded

lora16 [44]

Answer:

Elaina just began working as an occupational therapist assistant for $21.00 per hour. For each paycheck she receives, 12% is deducted from the gross pay for Federal Withholding Tax. In addition, 1.45% is deducted for Medicare and 6.2% for Social Security. Below is Elaina’s paycheck with missing information.

Elaina’s gross pay for a two week period is $1680.00, what is her net pay?

Step-by-step explanation:

3 0

2 years ago

Let event A = You buy a new pair of gloves on Saturday. Which event is most

Salsk061 [2.6K]

Answer:

C_ You finished a book on thursday.

Hope this helps

7 0

3 years ago

An object dropped from a height of 600 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t)=600 - 16t^2

gulaghasi [49]

Answer:

t as a function of height h is t = √600 - h/16

The time to reach a height of 50 feet is 5.86 minutes

Step-by-step explanation:

Function for height is h(t) = 600 - 16t²

where t = time lapsed in seconds after an object is dropped from height of 600 feet

t as a function of height h

replacing the function with variable h

h = 600 - 16t²

Solving for t

Subtracting 600 from both side

h - 600 = -16t²

Divide through by -16

600 - h/ 16 = t²

Take square root of both sides

√600 - h/16 = t

Therefore, t = √600 - h/16

Time to reach height 50 feet

t = √600 - h/16

substituting h = 50 in the equation

t = √600 - 50/16

t = √550/16

t= 34.375

t = 5.86 minutes

7 0

3 years ago