[tex]f(x) = - 2(x - 4) ^2 + 6[/tex]
what is the vertex of this function ?​

Answer:

33. y = -x² - 2x + 3

34. y = x² + 4x + 3

Equation of a parabola is given by y = a(x - h)² + k

where:

33.

Looking at the graph find the vertex, vertex is at (-1, 4)

Take one point: (1, 0)

Substitute (h, k) = (-1, 4) and (x, y) = (1, 0) into equation to find value of a:

Now equation:

y = a(x - h)² + k

y = -1(x - (-1))² + 4

y = -(x + 1)² + 4

y = -(x² + 2x + 1) + 4

y = -x² - 2x - 1 + 4

y = -x² - 2x + 3

34.

The vertex is at (h, k) = (-2, -1) and the curve passes through (x, y) = (0, 3)

Find value of a:

Now equation:

y = a(x - h)² + k

y = 1(x - (-2))² - 1

y = 1(x + 2)² - 1

y = (x² + 4x + 4) - 1

y = x² + 4x + 3

Answer:

[tex]\textsf{33.} \quad y=-x^2-2x+3[/tex]

[tex]\textsf{34.} \quad y = x^2+4x+3[/tex]

Step-by-step explanation:

Factored form of a quadratic equation:

[tex]\boxed{y=a(x-r_1)(x-r_2)}[/tex]

where:

From inspection of the graph:

Substitute the roots and the vertex into the formula and solve for [tex]a[/tex]:

[tex]\begin{aligned}y & =a(x-r_1)(x-r_2)\\\implies 4 & = a(-1-(-3))(-1-1)\\4 & = a(2)(-2)\\4 & = -4a\\-4a & = 4\\\dfrac{-4a}{-4} & = \dfrac{4}{-4}\\a & = -1\end{aligned}[/tex]

Substitute the found value of [tex]a[/tex] and the roots into the formula and rewrite in standard form:

[tex]\begin{aligned}y & =a(x-r_1)(x-r_2)\\\implies y & = -1(x-(-3))(x-1)\\y & = -(x+3)(x-1)\\y & = -(x^2+2x-3)\\y & = -x^2-2x+3\end{aligned}[/tex]

Therefore, the equation of the parabola in standard form is:

[tex]y=-x^2-2x+3[/tex]

Vertex form of a quadratic equation:  

[tex]\boxed{y=a(x-h)^2+k}[/tex]

where:

From inspection of the graph:

Substitute the vertex and y-intercept into the formula and solve for [tex]a[/tex]:

[tex]\begin{aligned}y & = a(x-h)^2+k\\\implies 3 & = a(0-(-2))^2+(-1)\\3 & = a(0+2)^2-1\\3 & = 4a-1\\3 +1& = 4a-1+1\\4 & = 4a\\4a & = 4\\\dfrac{4a}{4} & = \dfrac{4}{4}\\a & = 1\end{aligned}[/tex]

Substitute the found value of [tex]a[/tex] and the vertex into the formula and rewrite in standard form:

[tex]\begin{aligned}y & = a(x-h)^2+k\\\implies y & = 1(x-(-2))^2+(-1)\\y & = (x+2)^2-1\\y & = (x+2)(x+2)-1\\y & = x^2+4x+4-1\\y & = x^2+4x+3\end{aligned}[/tex]

Therefore, the equation of the parabola in standard form is:

[tex]y & = x^2+4x+3[/tex]

Answer:

It’s A took test

Step-by-step explanation:

Answer: I'm pretty sure it's A!

Step-by-step explanation: It's on Edge, hope this helped :)

Answer:

you dont have 7 to 11

Step-by-step explanation:

13.a

15.a

12.i

14.h

Answer:

The answer is that Alex wrote checks for 42.50 more than the amount he had.

Step-by-step explanation:

If he has -42.50 that means he owes the bank 42.50 the only way he would owe the bank that much is if he spent 42.50 that he didn't have.

Answer:

Step-by-step explanation:

Let the number of games be x

Inequality:

Since there should be more than 0 left, another inequality for it:

So 13 < x < 15, which leaves us with 14

Answer:

x = 15

Step-by-step explanation:

4/5x - 9 = 3

add 9 to both sides

4/5x = 12

multiply both sides with 5/4

(4/5x)5/4 = 12(5/4)

x = 15

9514 1404 393

Answer:

  1 scoop

Explanation:

There are 16 tablespoons in 1 cup, so Xander uses (1/8)·(16 tbsp) = 2 tbsp of topping for each scoop of ice cream.

For 1 scoop of ice cream, Pedro will use 1+1 = 2 tbsp of topping.

Hence, both use the same amount of topping (2 tbsp) for 1 scoop of ice cream.

Answer:

It's 9

Step-by-step explanation:

2x+10=3x+1

-x=-9

x=9

The value of h(3) will be equal to -18.

What do you mean by domain and ranges of a function ?

The domain is the set of all values for which the function is defined and the range of the function is the set of all values that function takes.

As per the question ;

Given function is ;

h(x) = -5x - 3

Here , we have to find out the value of h(x) for x = 3 , and this can be solved if we put the value of x in the expression x - 3.

We know that a function is defined for domain and range , so we have to give a domain here which is x = 3.

So , for x = 3 ;

h(3) can be calculated as follows ,

=(-5 × 3 ) - 3

Firstly we will solve the term within the parentheses.

= -15 - 3

and now we will add both the negative terms and we will get the value  of h (3) which is ,

= -18

Thus , the value of h(3) will be equal to -18.

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Answer: 475 inches

Step-by-step explanation:

if we have 100 tiles and each is 4.75 inches wide

100*4.75=475 inches

Answer:

The answer is 32.63

Step-by-step explanation:

Answer:

= −26.97

Step-by-step explanation:

Answer:

0.0794%

Subtract the 26.3 from 100 and get the amount for water giving you 73.7

Divide both from their molar masses

26.3/74.55=0.3528

73.7/18.016=4.0908

Add both answers, 0.3528+4.0908=4.4436

Divde the KCl total from the the total moles which gives you your final amswer

0.3528/4.4436=0.0794

Answer: 0.0794

Step-by-step explanation:

Answer:

C or A I think it's correct

The Bridge A' main span is 60% shorter than the span of the Bridge B.

The percentage is the difference between two parameters divided by the average of those values.

Now, as per the given question;

Bridge A' span = 2800 feet.

Bridge B' span = 4500 feet.

Percentage difference in span length :

[(difference in span) / span of B] × 100%

Difference in span = 4500 - 2800 = 2700

Now, calculate the percentage difference;

Percentage difference = (2700 / 4500) × 100%

Percentage difference = 0.6 × 100% = 60.0 %

Therefore, the main span of the Bridge B is 60% longer than the main span of bridge A.

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Answer:

1.99677419355

Step-by-step explanation:

Answer:

1.996 rounds to 2

Step-by-step explanation:

Answer:

−1 /10 x+4

Step-by-step explanation:

Group like terms

=3/5x-7/10x+12-8

add

-10x+12-8

1/10x=x/10

-x/10+12-8

−1 /10 x+4

If you need more help just ask

Answer:

I think C

Step-by-step explanation:

Answer:

Actually I think it would be 2 1/3

Step-by-step explanation:

18 goes into 8 twice right, so whole number 2 with 2 left over so that makes it 2 2/6 then 2/2 and 6/2 is 1 and 3 so 2 1/3.

Answer:

x = 32

Step-by-step explanation:

x - 7 = 25

To solve equations, you do the some thing to both sides to isolate x.

After adding 7 to both sides we have:

x = 32

Answer:

x = 32

Step-by-step explanation:

⇒ Isolate the variable x by adding 7 to both sides:

x – 7 + 7 = 25 + 7

⇒ Evaluate the equation to finally get:

x = 32

Hope this helps! :)

The probability of getting the sum 5 on the faces of both dice is 1/9.

Probability is a branch of mathematics that deals with numerical descriptions of just how likely an occurrence is to occur or how likely a proposition is to be true.

Probability (event) = favourable outcome/ total outcome.

There are 36 possible outcomes when rolling two dice. Keep in mind that now the "sample space" is a set that includes all possible outcomes.

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

The sample space for getting the sum as 5 on both faces is;

S = {(4,1), (3,2), (2,3), (1,4)}

Thus, the favourable outcome is 4

The total outcome is 36.

P (sum as 5) = favourable outcome for 5/total outcome

P (sum as 5) = 4/36

P (sum as 5) = 1/9

Therefore, the probability that sum is 5 on both the faces of dice is 1/9.

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Answer:8(2g+1)(4g2-2g+1)

Step-by-step explanation:

3.63/34= 0.1067647058823...

that means each oz of soda is 10.7 cents