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Answer:

Part A

The equation of the parabola in standard form is f(x) = 0.5·x² + x - 7.5

Part B

The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)

Step-by-step explanation:

The coordinates of the vertex of the parabola, (h, k) = (-1, -8)

The zeros of the parabola = -5, 3

Part A

The quadratic equation representing the parabola can be written as follows;

y = a·(x - h)² + k

The standard form of the equation is f(x) = a·x² + b·x + c

k = c - b²/(4·a)

h = -b/(2·a)

c = k + a·h² = -8 + a

From the zeros of the parabola, we have;

f(-5) = a × (-5)² + b×(-5) + c = 25·a - 5·b + c = 0

f(3) = a × (3)² + b×(3) + c = 9·a + 3·b + c = 0

Therefore, we have;

25·a - 5·b + c = 0...(1)

9·a + 3·b + c = 0...(2)

From which we have;

25·a - 5·b + c = 25·a - 5·b - 8 + a = 26·a - 5·b - 8 = 0

9·a + 3·b + c = 9·a + 3·b - 8 + a = 10·a + 3·b - 8 = 0

We then have;

26·a - 5·b = 8...(3)

10·a + 3·b = 8...(4)

Making 'b', the subject of both equations (3) and (4), equating the values, we find the value of 'a' as follows;

From equation (3), we have;

26·a - 5·b = 8

∴ b = (26·a - 8)/5

From equation (4), we have;

10·a + 3·b = 8

∴ b = (8 - 10·a)/3

From b = b, by transitive property, we have;

(26·a - 8)/5 = (8 - 10·a)/3

3 × (26·a - 8) = 5 × (8 - 10·a)

78·a - 24 = 40 - 50·a

∴ 128·a = 64

a = 64/128 = 1/2 = 0.5

a = 0.5

∴ b = (26·a - 8)/5 = (26 × 0.5  - 8)/5 = (13 - 8)/5 = 1

b = 1

c = -8 + a

∴ c = -8 + 0.5 = -7.5

c = -7.5

The equation of the parabola in standard form is therefore presented as follows;

f(x) = 0.5·x² + x - 7.5

Part B

The equation of the parabola in factored form is given as follows;

With the aid of a graphing calculator, we have;

f(x) = 0.5·x² + x - 7.5 = 0.5×(x² + 2·x - 15) = 0.5·(x + 5)·(x - 3)

The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)

Answer:

Look at the graph bellow

Step-by-step explanation:

use the slope and y-intercept to graph.

Answer:

I thinks its D.

Step-by-step explanation:

Answer:

100°

Step-by-step explanation:

Since x and the 100 degree angle which is highlighted in blue are vertical to each other, they are parallel to each other as it is vertically opposite angles.

If they are parallel, it means

Angle highlighted in blue = 100°

x = 100°

Answer:

247.728

Step-by-step explanation:

(3.97)(62.4)

=247.728

Answer:

growth

Step-by-step explanation:

1.034 < 1 means the number will get larger

Answer:

Step-by-step explanation:

Since the ratio or rate is greater than one this is an exponential growth function

Answer:

do you need an equation? if so it would be 2x+40

Step-by-step explanation:

Answer:

1/2m - 4

Step-by-step explanation:

Answer: The second one, 10 rolls for $12. 1.29 (Rounded)

Step-by-step explanation:

14/18 is 1.29 (Rounded)

10/12 is 1.20.

The unit rate is cheaper, therefore making it the better buy

Answer:

Step-by-step explanation:

multiply 7 times 4 then you add that when you

add 4+1=5 then you multiply those two

Answer:

[tex]x = 64 + 45 \\ x = 109[/tex]

Answer:

You were correct.

Step-by-step explanation:

If the input to the function y = 4x - 3 is 2 Then

y = 4 * 2 - 3

= 8 - 3

= 5

Hope it helps :)

Answer:

25

Step-by-step explanation:

150 divided by 30 times 5

Hope this helps. I May be wrong though.

Answer:

I think it is 73

Step-by-step explanation:

Because i tryed all of the other numbers and they didnt work

HOPE THIS HELP !!!!!!!!!!!!!!!! :)

Answer:

Step-by-step explanation:

Increase by 23%

1.23 is the answer

Answer:

2/4=4/8

Step-by-step explanation:

you do 2×2=4 and 4×2=8. You multiply both denominators by 2.

Answer:

so you answered your own question?

Answer:

1296

Step-by-step explanation:

Answer:

what i dont understand the word

Answer:

its B

Step-by-step explanation:

Answer:

$200

Step-by-step explanation:

Hey There!

So first we want to find the price of each pound of banana

To do this we divide the cost by amount of bananas bought

86/43=2

so each pound of bananas cost $2

now we just multiply 2 and 100

2x100=200

so 100 pounds of bananas would cost $200

hope this helps :)

Answer:

50

Step-by-step explanation:

Calculate how much 1lbs of bananas cost by dividing 86 by 43. getting you 2. That means each lbs of bananas is $2. Then divide $100 by $2 getting you 50 because you have $100. So you can get 50lbs of bananas with $100.

Option A  is the correct answer because the ratio between the opposite side and the hypotenuse side is correct.

Triangle :

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle. The right triangle plays an important role in trigonometry. Let us learn more about this triangle in this article.

A triangle with Side lengths a unit, b units, and c units.

"Opposite" is opposite to the angle θ

"Adjacent" is adjacent (next to) to the angle θ

"Hypotenuse" is the long one

A)

Sin 55 = a/c

Sin  θ = opposite / hypotenuse

Option A ) is correct  Sin 55 = a/c  

B)

Cos(55°)=c/b

Cos θ =  Adjacent / hypotenuse

Cos 55 = c/ b is not equal to the Adjacent / hypotenuse

Option B)  is not a correct answer because the ratio is between  Adjacent and Hypotenuse.  

C)

Cos(55°)=a/b

Cos θ =  Adjacent / hypotenuse

Cos 55 = a/ b is not equal to the Adjacent / hypotenuse

Option C)  is not a correct answer because the ratio is between Adjacent and Hypotenuse.  

D)

Tan(55°)=c/a

Tan θ  = Opposite / Adjacent

Tan 55 =  c/a is not equal to the  Opposite / Adjacent

Option D)  is not a correct answer because the ratio is between Opposite and Adjacent.  

Learn more about Trignometry : brainly.com/question/22986150

#SPJ1

Answer:

Richie should add the number 36 to both sides.

Step-by-step explanation:

To complete the square, you need to divide b by 2, square it, then add it to both sides. In this case, you'd do this:

12/2=6

6^2=36

Answer:

d is correct i think

Step-by-step explanation:

My brain aint working

Answer:

320 i think lol

Step-by-step explanation:

Answer:

3.56

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation: