Mathematics High School


f(x) = -x^2+ 6x -10
write each function in vertex form and give the vertex

Answers

Answer 1

Answer:

Vertex form: f(x) = – (x – 3)² – 1  

vertex: (3, -1)

Step-by-step explanation:

Given the quadratic function, f(x) = -x²+ 6x -10:

where a = -1, b = 6, and c = -10

The vertex of a parabola is the point at which the parabola intersects the axis of symmetry. The axis of symmtery occurs at x = h. Therefore, the x-coordinate of the vertex is the same as h.

To find the vertex, (h, k), you need to solve for h by using the formula:  [tex]h = \frac{-b}{2a}[/tex]

Plug in the values into the formula:

[tex]h = \frac{-b}{2a}[/tex]

[tex]h = \frac{-6}{2(-1)} = 3[/tex]

Therefore, h = 3.

Next, to find the k, plug in the value of h into the original equation:

f(x) = -x²+ 6x -10

f(x) = -(3)²+ 6(3) -10

f(x) = -1

Therefore, the value of h = -1.

The vertex = (3, -1).

Now that you have the value for the vertex, you can plug these values into the vertex form:

f(x) = a(x - h)² + k

a =  determines whether the graph opens up or down, and makes the parent function wider or narrower.

If a is positive, the graph opens up.If a is negative, the graph opens down.

h = determines how far left or right the parent function is translated.

k = determines how far up or down the parent function is translated.

Plug in the vertex, (3, -1) into the vertex form:

f(x) = – (x – 3)² – 1  

This parabola is downward-facing, with its vertex, (3, -1) as its maximum point on the graph.

Related Questions

b(n)=−4−2(n−1)

find the 12th term in the sequence.

Answers

Answer:

-18

Step-by-step explanation:

b(12) = 4 - 2(12-1)

= 4 - 2(11)

= 4 - 22

= -18

negative signed solution of (x+9)^2=-9
also, what changes because of "negative signed solution"

Answers

ANSWER:

18

_______________

HOPE IT HELPS YOU

CAN YOU BRAINLEST ME

Solve the quadratic equation
d²-5d+6=0

Answers

Answer:

BBC

Step-by-step explanation:

Answer:

d = 6       d = -1

Step-by-step explanation:

Use displacement to factor

d²-5d+6=0

d²+d-6d-6=0

d(d+1)-6(d+1)=0

(d-6)(d+1)=0

d-6=0 or d+1=0

d = 6       d = -1

Please help i reward brainliest
plz no silly answers

Answers

Answer:

64, -64, -64

-27, 27, 27

Step-by-step explanation:

If x = 4,

x³ = 4³ = 64

-x³ = -4³ = -64

(-x)³ = (-4)³ = -64

If x = -3,

x³ = -3³ = -27

-x³ = -(-3)³ = 27

(-x)³ = (-(-3))³ = 27

what is the sign of a • (-b/b) when a = 0 and b < 0?

Answers

Answer:

gimmie my points boi

Step-by-step explanation:

eiurfh4iewurhfwo8rho

PLEASE HELPP!! Type an equation for the
following pattern. Make sure
the fraction is in simplest form.

Answers

Answer:

y = -3/2x + 10.5

Step-by-step explanation:

You can plug in the x values and you'll get the y values of the table. Hope this helps :)

2/3x=4

Group of answer choices

a. x= 8

b. x= 6

c. x = 8/3

Answers

b, x=6

i already did this and this was the answer

please help I will make you Brainliest if correct (show working)​

Answers

1.) X= 4m - 1.2m = 2.8m

Split the irregular shape into 2 (A and B)

A= 4m x 3.8m = 15.2m^2

B= 3m x 2.8m = 8.4m^2

2.) Total area = A + B
= 15.2 + 8.4 = 23.6m^2

if 3x - 2y = 9 , 27x³- 8y³= 1377 , prove that xy = 4



plzz answer this question... ​

Answers

Step-by-step explanation:

Here we are given that , the Value of

[tex] 3x - 2y = 9 [/tex] [tex] 27x^3 - 8y^3 = 1377 [/tex]

And we need to find the prove that ,

[tex] xy = 4 [/tex]

We know a identity as ,

[tex] (a-b)^3 = a^3-b^3-3ab(a-b) [/tex]

On cubing both sides of the given equation,

[tex] (3x-2y)^3 = 9^3 [/tex]

Simplify and then substitute ,

[tex] 27x^3-8y^3 -3(3x)(2y)(3x-2y ) = 729[/tex]

[tex] 1377 - 18xy (9) = 729 [/tex]

[tex] 162xy = 1377-729 [/tex]

[tex] xy =\dfrac{648}{162}[/tex]

[tex]xy = 4 [/tex]

Hence Proved !

I NEED HELP FAST! WHOEVER GETS RIGHT GETS BRAINLY Explain how to evaluate the expression 4x+10 for x=5.

Answers

Evaluating expressions involve substituting the given value for x into the equation.

If x = 5:

4x + 10 = 4(5) + 10 = 20 + 10 = 30

Therefore, 4x + 10 = 30 when x = 5.

please help I dont understand ​

Answers

Step-by-step explanation:

When it says y varies directly with x it just means that y and x are proportional/equal to each other. The constant of variation and the constant of proportionality are the same thing just different way of saying it so they can confuse you and make your life miserable. Since y and x are proportional to each other and the constant of proportionalty is -5 to make an equation that represents a line you use the formula y=mx+b. That is the slope of the line. With that formula let's first plus in the x so we have y=m2+b. The formula for direct variation is y=kx as well that's good to know and it's good to memorize all these formulas. Math becaomes easier when you have the process down pat and you just need to plug numbers into different equations, expressions, and scenarios. Do m = [y1 - y2] / [x1 - x2] and you'll get the answer.

What is the value of {-12}
–13
–12
12
13

Answers

Answer: B. -12

Edge 21: Since the brackets are facing down, there is no need to round the -12 because it's already an integer.

i need help ASAP!! will mark brainliest. I need to find the vertex of this problem but i don’t know how to work/solve it, pls help! thanks!!

Answers

the answer is b i took the quiz

will give BRAINLIEST!!!!!!
3 3/4 X 1 2/5 do a step by step explanation please and also you have to make it so you convert it into an improper fraction first... please answer!!!

Answers

Answer:

5 1/4

Step-by-step explanation:

To convert into an improper fraction, we times the whole number by the denominator and then add the numerator. For the first number, it is 15/4 and the second number is 7/5. Then we multiply 15/4 and 7/5 to get 5 1/4.

Answer:

99/5

Step-by-step explanation:

CONVERT INTO:

33/4 x 12/5

MULTIPLY THE FRACTIONS:

(33x12)

--------------

5

CANCEL TERMS:

(33x3)

-----------

5

SIMPLIFY:

99/5

Select the correct answer.
Which statement is true about the graph of this equation?

y + 4 = 4(x + 1)

A.
The graph is a line that goes through the points (1,-4) and (0,0).
B.
The graph is a line that goes through the points (1,4) and (2,8).
C.
The graph is a line that goes through the points (-4,-1) and (-3,-3).
D.
The graph is a line that goes through the points (4,1) and (5,5).

Answers

The answer is B
I hope this helped you !!

Answer:

A

Step-by-step explanation:

The graph is a line that goes through the points (1,-4) and (0,0)

If you receive $68 for mowing lawns for 8 hours. What would be the equation to find out how much money you would receive in an hour?

Answers

Answer:

$68÷8= x money per hour

Step-by-step explanation:

3(x+1)=2(x-3) whats the answer

Answers

The answer is -9

I dont know the step-by-step used a calculator

Can you translate the measurements to (cups, teaspoons, tablespoons etc.)

Top flour 170g
Baking powder 5g
Sugar 10g
Butter 40g
Maple syrup 30ml
Milk 40ml

Answers

Answer:

Flour: 18.76 Tablespoons

56.28 Teaspoons

1.17 U.S. Cups

Baking Powder: 0.35 Tablespoons

1.04 Teaspoons

0.02 U.S. Cups  

Sugar: 0.80 Tablespoons

2.40 Teaspoons

0.05 U.S. Cups

Butter: 2.82 Tablespoons

8.46 Teaspoons

0.18 U.S. Cups

Maple Syrup:

0.127 Cups

2.029 Tablespoons

6.087 Teaspoons

Milk:

0.169 Cups

2.705 Tablespoons

8.115 Teaspoons

Hope this helps!!

Have A Blessed Day <333

Match the situation to the most appropriate graph #7

Answers

Graph K. This is because the cost of a gallon of milk is not increasing constantly, as in a linear rate, but it has only increased a few times in a year. Therefore, graph K shows that a gallon of milk is a steady, unchanged price, then the cost rises and stays the same, then rises again and stays the same. So, it is not a linear graph because the cost of the milk is not going up at a constant rate.

3. Which table has a constant of proportionality equal to 2.5?
x
х
y
X
0
0
2.5
os
2.5
NO
1
2
.
5
7.5
А
о
B
х
y
2
у
2.5
3.75
W NX
2
5
3
3
7.5
10
4
ch
5
4
D

Answers

Answer:

your answer is A

I can assure you that you will give brainlest

Answer:

A

Step-by-step explanation:

Can someone help me with these two? Please

Answers

For 16/18 it would be 8/9
For 10/15 it would be 2/3

Answer:

8/9 and 2/3

Step-by-step explanation:

find common factor with each of the numbers and divide by that

16 and 18, 2 is the gcf.

16/2=8   18/2=9

the gcf in the second one is 5.

10/5=2  15/5=3

Hope this helps!

ANSWER THIS ASAP PLEASE !

Answers

Simple the answer is: n=14

2n-3=25
We can move the divided by to other side of equal sign and it now because multiply by 5.
2n=28
We add 3 to both sides of equal sign
n=14
We divide 2 to both sides of equal sign to get the variable by itself
Your answer is : n=14

Write the prime factorization of 42. Use exponents when appropriate and order the factors from least to greatest

Answers

42: 2,3,7
2 x 3 x 7 = 42

Answer:

42 = 2*3*7

Step-by-step explanation:

42 can be rewritten as 2*21, for example.  

2 is prime.  21 = 3*7.

Then 42 = 2 * 21 is also equal to:

         42 = 2*3*7. where these factors are ordered from least to greatest.  The prime factors of 42 are {2, 3, 7}.

Can someone help me and if you don’t have the answer don’t answer cause you’re just wasting my time

Answers

Answer: 1 is 534

Step-by-step explanation:

explain and show how please ! and give answer someone pls answer asap !

Answers

Answer:

Both angels are 70 and both added are 140.

Step-by-step explanation:

Because of the rules, that's names i never remember angle 1 and angle 2 are both 70° and obiously they equal 140.

how do you solve a no solution equation

Answers

Answer:

to solve a no solution equasion, you solve it like any other question. 4 example 3 +7 = 10 so 3 + _ = 10 its the same

Step-by-step explanation:

maths help me maths giving 10 point​

Answers

Step-by-step explanation:

[tex]x-2>4[/tex]

[tex]x>6[/tex]

And

[tex]3x+1\leq 28[/tex]

[tex]3x\leq 27[/tex]

[tex]x\leq 9[/tex]

So [tex]x[/tex] ∈ [tex](6, 9][/tex]

Please give me a brainliest answer

Jerry played with 3 friends today, all at different times. He played with Tommy for 1 7/8 hours, then Nathan for 1 3/4 hours, then Chris for 3/2 hours.
How many hours did Jerry play with his 3 friends today?

Answers

Answer:

4hrs 7 minutes and 30 seconds

Step-by-step explanation:

1 7/8 = (1=60) + (7/8 * 60) = 1 : 52:50 time played with Tommy   1 3/4 = (1=60 ) ( (3/4 * 60) = 1:45:00 time played with Nathan   3/2 = (3/2 *60) = 90 = 1:30:00 time played with Chris    Total played with 3 friends = 1:52:50 + 1:45:00+1:30:00= 4:07:50 = 4hrs 7 minutes and 30 seconds

help please, im confused​

Answers

Answer:

same sir sorry can't help you ok bye sorry

5.5.WW3
Question Help
Find the quotient
30)593
Select the correct choice below and fill in the answer box(es) within your choice.
OA. The quotient is
OB. The quotient is
R

Answers

19.7666
Because it just makes since I think
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