A ball is thrown straight up from the height of 3 ft with a speed of 32 ft/s. It’s height above the ground after x seconds is given by the quadratic function y = -16x^2+32x+3.
Explain the steps you would use to determine the path of the ball in terms of a transformation of the graph of y=x^2.

Answer:

The given equation has a y-intercept at (0, 3).

y = -16x^2 + 32x + 3 = -16(x^2 - 2x) + 3 = -16(x - 1)^2 + 19. This means the vertex is at (1, 19).

To transform the y = x^2 graph:

First we invert the graph with respect to the x-axis, maxing it a downward parabola y = -x^2.

Next, we move its vertex from the origin (0, 0) to (1, 19), making the equation y = -(x - 1)^2 + 19.

Third, we "expand" the opening of the parabola such that it passes through the y-intercept of (0, 3). The right-side of the parabola should also be expanded similarly, since it is symmetric.

would the answer be
2x+12 ​

for m(x)=-2x+7, find the value of x for which m(x)=13

Ethan had his two friends over for pizza. Ethan ate 1/4 of the pizza. One of his friends ate 3/8 of the pizza and the other friend ate 1/8 of the pizza. How much of the pizza is left?​

A lawn moving company is trying to grow its business. It had 18 clients

The math department needs to buy new textbooks and laptops for the computer science classroom. The textbooks cost $116.00 each, and the laptops cost $439.00 each. If the math department has $6,500 to spend and purchases 30 textbooks, how many laptops can they buy

I have a time limit please hurry!

Complete the sentence about the relation. Enter only numbers and commas, do not use spaces!


The domain of the relation is {
} and the range of the relation is {
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A factory uses 1/8 of a barrel of raisins in each batch of granola bars. Yesterday, the factory used 3/4 of a barrel of raisins. How many batches of granola bars did the factory make yesterday?

At the beg ending of 2009 Marilyn invested $5000 in a savings account account pays 4% interest per year at the end of the year at the interest is paid how much does Marilyn have in the account?

what is 20% of 240 check your mah plz help give brainy is

Lily has already jarred 1 liter of jam and will jar an additional 4 liters of jam every day. Write
an equation that shows the relationship between the days d and the jam made j.
Write your answer as an equation with j first, followed by an equals sign.

Will mark brainliest if correct

In a theater, there are 4 long rows of chairs, each with an equal number of chairs. There are 5 short rows of chairs, each with an equal number of chairs. On a crowded day, the ushers added 2 chairs to each long row and 3 chairs to each short row.

If x represents the number of chairs in each long row and y represents the number of chairs in each short row, the total number of chairs in the theater is given by the expression 4(x + 2) + 5(y + 3).

Select the true statement

2.5 pounds of blueberries cost $11.25

11.25 pounds of blueberries cost $2.50

2.25 pounds of blueberries cost $0.50

1 pound of blueberries cost $5.00

is 1x + 34 bigger than 25?

Which graph has a rate of change of zero?

Please help will give brainliest 19-26

I don’t understand graphs that much , i probably would know this if i was in school but im online

iv) You have 10 gallons of lemonade to sell (1 gallon = 3785 cm3). Each customer
uses one paper cup. How many paper cups will you need?

(2/3)m tm= a + r, for m

At the end of the season, 4 basketball teams in a league are having a pizza party at a restaurant. Team Number of People Sharks 17 Wolves 21 Tigers 20 Hawks 17 Coaches 9 The restaurant manager suggests that they order one pizza for every 6 people. How many pizzas should they order? Enter your answer in the box. its confuzing

Sean has 9 liters of juice. He pours equal amounts of the juice into 4 pitchers. There is 0.5 of a liter of juice left. How many liters of juice are in each pitcher? Sean has 9 liters of juice. He pours equal amounts of the juice into 4 pitchers. There is 0.5 of a liter of juice left. How many liters of juice are in each pitcher?

plz i will give u 38 to 48 points plzzzzzzzz

GUYS THIS IS DUE SOON I NEED HELP

A small business has 50 total employees: 35 part-time and 15 full-time. What percent of the employees are full-time?

Rani bought 3 shirts for $9 each. Which equation can be used to find the total cost of the shirts, c?

2) If it is 12° outside and the temperature is going to
drop 19º. What will the new temperature be?

6x + 10 = 2(3x + 4)​

HELP I’m almost out of time ( it’s not Y=2x+4)

A town is going to use its property tax records to pick
people to take part in a focus group on water treatment
in the city. Everyone who owns a house or apartment
in the town will be listed in the property tax records.
These focus groups have been very popular, and everyone
selected to take part in the focus group actually does
take part. The town's aim is that everyone who lives in
the town has a chance to take part in the focus group.
What problems, if any, do you see with this sampling
method?
A nonresponse
B. response bias
c. undercoverage
D. there are no problems with this sampling method

Identify the slope & y-intercept for the following equation: y=-5x-3

The sea surface temperatures range from -2 degrees Celsius to 31 degrees. Determine the difference between the maximum and minimum temperatures.