Answer:
1. The vertex of the graph of the function is (-4, 7)
2. The vertex represents a minimum value
3. The equation represented by the new graph is g(x) = (x + 4)² + 1
Step-by-step explanation:
The given quadratic function is given in vertex form, y = a·(x - h)² + k, as follows;
g(x) = (x + 4)² + 7
1. By comparing the given quadratic function and the vertex form of a quadratic equation, we have;
a = 1, h = -4, and k = 7
The vertex of the graph of the function, (h, k) = (-4, 7)
2. Given that a = 1 > 0, the graph of the quadratic function opens upwards and the vertex represents a minimum value
3. Shifting the graph 6 units down from where it is now will give;
The vertex = (h, k - 6) = (-4, 7 - 6) = (-4, 1)
h = -b/(2·a), k = (-b²/(4·a) + c = -a·h² + c
c = k + a·h²
Therefore, initial value of the constant term, c = -1×(-4)² + 7 = 23
After the shifting the graph 6 units down, c = 23 - 6 = 17
∴ k = 1 = -a·(-4)² + 17
∴ -16/16 = -1 = -a
a = 1
Therefore, the equation represented by the new graph is g(x) = (x + 4)² + 1.
1. The vertex of the graph of the function is (-4, 7)
2. The vertex represents a minimum value
3. The equation represented by the new graph is g(x) = (x + 4)² + 1
What is a graph?
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The given quadratic function is given in vertex form, y = a·(x - h)² + k, as follows;
g(x) = ( x + 4 )² + 7
1. By comparing the given quadratic function and the vertex form of a quadratic equation, we have;
a = 1, h = -4, and k = 7
The vertex of the graph of the function, (h, k) = (-4, 7)
2. Given that a = 1 > 0, the graph of the quadratic function opens upwards and the vertex represents a minimum value
3. Shifting the graph 6 units down from where it is now will give;
The vertex = (h, k - 6) = (-4, 7 - 6) = (-4, 1)
h = -b/(2·a), k = (-b²/(4·a) + c = -a·h² + c
c = k + a·h²
Therefore, initial value of the constant term, c = -1×(-4)² + 7 = 23
After the shifting the graph 6 units down, c = 23 - 6 = 17
∴ k = 1 = -a·(-4)² + 17
∴ -16/16 = -1 = -a
a = 1
Therefore, the equation represented by the new graph is g(x) = (x + 4)² + 1.
To know more about graphs follow
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Joe is saving for a new online video game. He has some money already in his savings, and he can add $2.50 each week. This relationship is shown in the graph. Write an equation and explain what the slope and the y-intercept mean in this situation?
Answer: Y=2.50x+b
Step-by-step explanation:
Thats not the whole answer, you didnt attach the graph but what you need to do is find the y-intercept and put that into b and theres your equation. The y-intercept(B) represents the initial money that joe had in his savings the 2.50x part or the slope is the money that he states he can add each week.
Answer:
slope is how much money joe adds to his account savings each week
the y intercept is the money he had before he started waiting
for the equation the slope is $2.50 and the y intercept is where the line hits the y axis but because you don't have a graph I don't know how to help you with this part, maybe someone else can!
hope this helps!
What is the zero of the linear function graphed below?
Answer:
All lines, with a value for the slope, will have one zero.
Step-by-step explanation:
To find the zero of a linear function, simply find the point where the line crosses the x-axis. Zeros of linear functions: The blue line, y=12x+2 y = 1 2 x + 2 , has a zero at (−4,0) ; the red line, y=−x+5 y = − x + 5 , has a zero at (5,0) .
simplify and Express the the result in power notation with positive exponents
a) 2-³×(-7)-³
Answer:
-1/14³Step-by-step explanation:
Use properties:
aⁿbⁿ = (ab)ⁿa⁻ⁿ = 1/aⁿSimplify:
2⁻³*(-7)⁻³ =(2*(-7))⁻³ =(-14)⁻³ =-14⁻³ =-1/14³What interest will be charged on a $300 loan for 6 months if the rate is 18% simple interest?
23.90
318.00
© 540.00
© 27.00
324.00
Answer: 540.00
Step-by-step explanation:
Select all expressions that are equivalent to 6x +1 - (3x - 1)
Hint: Don't forget to distribute the negative!
6x +1 -3.2 - 1
6x + (-3x) +1+1
3x + 2
6x - 3x + 1 - 1
6x +1+(-3x) – (-1)
Remy walked to a friend’s house m miles away at an average rate of 4 mph. The m-mile walk home was at only 3 mph, however. Express as a fraction
a) Time Remy spent walking home.
b)Time Remy spent walking.
(Answer both (a) and (b).
Answer:
a) m/4 miles per hour
b) 7m/12 miles per hour
Step-by-step explanation:
Mathematically, at any point in time;
Time = distance/speed
The distance here at any point is m mph
a) For the time spent walking home
Time = m/4 miles per hour
b) We add the time walking to the friend’s house and the time that it took to walk home
That would be;
m/4 + m/3 = 7m/12 miles per hour
51:55
The phrase "six less than twice y" can be represented by the algebraic expression
2y-6
2y + 6
O 6<2y
6 > 2y
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someone please help me. please
5x+20 + 9x-92 = 180
x = 18
5(18)+20
<A = 110
GIven that GR= x+5 and GP= 2x-3 which expression below calculates the perimeter of this gate? (x+5) + (2x-3) (x+5) + (2x-3) 2(x+5)-2(2x-3) 2(x+5)-2(2x-3) (x+5)+(2x-3) (x+5)+(2x-3) 2(x+5)+2(2x-3)
Answer:
P = 2(x + 5) + 2(2x - 3)
Step-by-step explanation:
GIven that GR= x+5 and GP= 2x-3 which expression below calculates the perimeter of this gate?
The shape of the gate is rectangular.
Hence, the Perimeter of a rectangle (the gate) = 2L + 2W
Where :
L = GR = x + 5
W = GP = 2x - 3
Hence,the perimeter of the gate is
P = 2(x + 5) + 2(2x - 3)
0.0000078
convert to scientific notation
Answer:
7.8 x 10^-6 or 7.8E-6
Step-by-step explanation:
Answer: = 7.8 × 10-6
Step-by-step explanation: Hope this helps
Number 3 need the answer
Answer:
8
Step-by-step explanation:
one negative* one negative = always positive
what is the 4 digit code
Answer:
Try 4321
Step-by-step explanation:
If its not right lmk
If it is can I get brainliest pls
are the following lines parallel, perpendicular, or neither? explain
PLZ HELP WHOEVER ANSWERS THE MOST GETS ALL MY POINTS I HAVE 940 AND 5 BUCKS
Answer:
the answer is 1/4
Step-by-step explanation:
What is the slope of the line shown below?
Please help quick
Answer:
6/5
Step-by-step explanation:
You can see in the picture that when x goes up by 10, y goes up by 12. Since the formula for slope is change in y/change in x, you get 12/10 = 6/5
Answer:
I believe the awnser is A
Calculate the slope of the line passing through the two points: (3,-3) & (1,-7)
Answer:
3×1=3 _3×7=9
Step-by-step explanation:
hdjsdvUquwjsidhejeudxiwjekebebej
Which values of a, b, and c represent the answer in simplest form?
5 3
88
=a
a= 1,b=3,C= 2
a=1,b=40, C = 24
a= 1,b= 16,C= 24
a=1; b=2, c=3
Answer:
1 16/24 1 2/3 answer is D
Step-by-step explanation:
calculate the area of this triangle
Answer: 99 cm
Step-by-step explanation:
To calculate the area of a triangle, we use the formula:
A = H x B divided by 2
If we add our numbers shown, we get:
A = 18 x 11 = 198
198 ÷ 2 = 99
Therefore we get 99 as the answer.
Area = 99 cm
(Don't forget your unit)
simplify using the laws of exponents x^4 x^6
Answer: [tex]x^{10}[/tex]
If I Helped, Please Mark Me As Brainliest, Have A Great Day :D
42 yd
40 yd
What is the length of the hypotenuse?
C=
yards
HELP
Answer:
58 yards
Step-by-step explanation:
The Pythagorean Theorem states that:
[tex]a^{2} +b^{2} =c^{2}[/tex]
Where c is the hypotenuse, and a and b are the two legs of the right triangle. Substituting in 40 and 42 for a and b, respectively:
[tex]40^{2} +42^{2} =c^{2}[/tex]
Now, we isolate c:
[tex]c= \sqrt{40^{2} +42^{2} }[/tex]
Therefore, c is equal to 58, so the hypotenuse is 58 yards
Hope this helps!
Fnd the missng side length
Answer:
18m?
Step-by-step explanation:
Answer:
18 x 2 = 36 m
5 x 2 = 10 m
Step-by-step explanation:
2.5 x 2.5 = 5 m
9 x 9 = 18m
what is the inverse of F(x)= x^3+1
Answer:
[tex]f^{-1}[/tex](x)=[tex]\sqrt[3]{x-1}[/tex]
Step-by-step explanation:
Answer:
To find inverse, interchange the variables and solve for y
Step-by-step explanation:
(I put mines in a doc)
help ..
3(x+2)=5x+1-2x+5
Answer:
All real numbers are solutions
Step-by-step explanation:
Let's solve your equation step-by-step
3(x+2)=5x+1−2x+5
Step 1: Simplify both sides of the equation
3(x+2)=5x+1−2x+5
(3)(x)+(3)(2)=5x+1+−2x+5(Distribute)
3x+6=5x+1+−2x+5
3x+6=(5x+−2x)+(1+5)(Combine Like Terms)
3x+6=3x+6
3x+6=3x+6
Step 2: Subtract 3x from both sides
3x+6−3x=3x+6−3x
6=6
Step 3: Subtract 6 from both sides
6−6=6−6
0=0
Prove that the sum of five consecutive natural numbers is even
Answer:
Conversely, if n is divisible by 5, then n is the sum of five consecutive integers. In particular, this gives n = 5m + 10 = 5(m + 2) and, since m + 2 is an integer, this shows n is divisible by 5
Step-by-step explanation:
At the craft store, Kenji bought a bag of brown and blue marbles. The bag contained 60 marbles, and 40% of them were brown. How many brown marbles did Kenji receive?
evaluate the expression
(-4)^-3
asap, please
Answer:
Step-by-step explanation:
Here you go mate
Step 1
(-4)^-3 Equation/Question
Step 2
(-4)^-3 Simplify
1/-64
answer
1/-64 or -64
Whats 574 744 0213
times each other so join it
solve the question please ;)
Answer:
90,962,928
Step-by-step explanation:
50 POINT GIVEAWAY AND BRAINLEST FOR the FIRST ANSWER
Answer:
thank you
Step-by-step explanation:
Answer:
Step-by-step explanation:
<3
How do I find if it does work. If it does explain or if It doesn’t
Which expression is equivalent to 1
5(15 + 10x - 5)?
2 + 2x
2 - 2x
-2 + 2x
-2 - 2x
Answer:
2x + 2
Step-by-step explanation:
LOLOL☝️answer is up there☝️LOLOL