MATHEMATICS MIDDLE SCHOOL

Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.f(x)= 5x²-3.
g(x)= 5x²+3

Answers

Answer 1
Answer:

Answer:

see the explanation

The graph in the attached figure

Step-by-step explanation:

we have

Function f(x)

f(x)=5x^(2)-3 ----> equation A

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

The vertex is the point (0,-3)

The y-intercept is the point (0,-3) [value of y when the value of x is equal to zero]

The x-intercepts are the points

(-\sqrt{(3)/(5)},0) and  (\sqrt{(3)/(5)},0)

Function g(x)

g(x)=5x^(2)+3 ----> equation B

This is a vertical parabola open upward (because the leading coefficient is positive)

The vertex is a minimum

The vertex is the point (0,3)

The y-intercept is the point (0,3) [value of y when the value of x is equal to zero]

The function don't have x-intercepts (the roots are complex numbers)

We can say that the function g(x)  is the translation of the function f(x) 6 units up

using a graphing tool

The graph in the attached figure
Answer 2
Answer:

The graphs of these quadratic functions are similar in shape, with the main differences being vertical shifts and y-intercepts. The graph of g(x)=5x^2 +3 is obtained by shifting the graph of f(x)=5x^2 −3 upward by 6 units.

The graphs of the quadratic functions f(x)=5x^2 −3 and g(x)=5x^2 +3

Both functions are quadratic, which means they have a graph in the shape of a parabola. The coefficient of the x^2  term in both functions is 5, indicating that the parabolas open upwards.

Now, let's analyze the differences:

Vertical Shift:

For f(x)=5x^2 −3, there is a vertical shift downward by 3 units due to the constant term -3.

For g(x)=5x^2 +3, there is a vertical shift upward by 3 units due to the constant term +3.

Y-Intercept:

The y-intercept of f(x) occurs when x=0, and f(0)=−3, so the y-intercept is (0, -3).

The y-intercept of g(x) occurs when x=0, and g(0)=3, so the y-intercept is (0, 3).

Overall Shape:

Both graphs have the same overall shape since the coefficient of the

x^2  term is the same in both functions.

Symmetry:

The parabolas are symmetric with respect to the y-axis, as changing

x to −x in the quadratic term does not affect the overall value of the function.

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The sales tax for an item was $14.80 and it cost $370 before tax.Find the sales tax rate. Write your answer as a percentage.

Answers

Answer:

Step-by-step explanation: 370+14.80= 384.80

When you add them together the answer is 384.80

Complete each equation below so that it shows equivalent fractions.Clear Check

3



=

4

12






1

2

=

3








2



=

4

Answers

Answer:

Step-by-step explanation:

12=3x4

3= 2+1

4= 2+2 or 2x2=4

Answer:

12=3x4

3= 2+1

4= 2+2 or 2x2=4

Step-by-step explanation:

Neli needs to cut 3 long boards into 9 smaller boards.The first is 10 ft, the second is 16 ft, and the third is 18 ft. The table lists the smaller boards Neli needs use a drawing to show how he can devide the 3 boards so there is no waste.

Answers

4.8 ft because you have to add up all the board lengths and then you divide by 9

Dan bought five new baseball trading cards to add to his collection .The next day his dog ate half of his collection .There are now only twenty nine cards left .How many cards did Dan start with?with equation and result

Answers


-- After dog ate 1/2 of the collection, there were 29 remaining.

-- Just before dog came along, there were (2 x 29) = 58 cards.

-- That was after Dan added 5 new ones.

-- Before he added the 5 new ones, there were (58 - 5) = 53 cards.

-- When this story began, Dan had 53 cards.


first you double 29

than subtract the 5 new cards

29  x 2 - 5

   58-5

your answer is 53

The perimeter of the top of a desk is 54 inches. If the length of the desk is 15 inches, what is the width of the desk?

Answers

54=2L+2W
54=30+2W
-30
24=2W
÷2
12=W

the size of a computer screen is measured along the diagonal. what is the approximate size measured to the nearest inch, of a 12 inch by 10.5 in computer screen

Answers

In this exercise we have to use the knowledge of pythagoras and triangles to calculate the size of a canvas, in this way we find that;

15.945 inch

So knowing that the Pythagorean formula is given by:

a^2=b^2+c^2

Substituting b and c for the values ​​informed in the exercise we find that:

a^2=144+110.25 \n a^2=254.25 \n a=15.945

See more about pythagoras at brainly.com/question/10174253
This uses pythagoras which is a^2=b^2+c^2. You need to find the diagonal which is "a". Therefore a^2=144+110.25 which equals 254.25 then square root it and you get 15.945
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