Maximum and Minimum Values of General Quadratic Functions

1. By expressing y = 2x^2 + 4x + 17 in the form y = a(x + b)^2 + C, where a, b, and c are constants, state the minimum value of y and the value of x at which this occurs. Hence, sketch the curve y = 2x^2 + 4x + 17
x =
y =​

Answer:

x=-1

y=15

Step-by-step explanation:

This works because completing the square is essentially demonstrating what g(x)  - where g(x) in this case = x^2 - would have to be translated by to give the function you have.

So by completing the square you have shown that the function you've been given has been shifted to the left by -1, stretched by a factor of 2 along the y axis and shifted up by 15.

Work out m and c for the line:
y = X – 2

Cody leaves his home and cycles 5y miles south, then cycles (2y + 10) miles east. Finally, he cycles (4y + 8) miles south and reaches his school. How far does Cody cycle (in terms of y)?

(7th grade math question)

Sales of the Xbox One increased from 10,000 to 18,500 in November. What was the percent increase?

A) 8.5%
B) 45.9%
C) 85%
D) 85.8%

please answer soon​

HI PLSS HELP THIS IS DUE IN 15 MINS AND PLS SHOW WORK TYY

find all the missing angles

Max made 20 out of 32 free throws. What is the experimental probability that he will make his next free throw attempt?

Uhhhh last question lol I have to match them

The aquarium opened at 8.00 am . In the first hour 140 people purchased admission tickets . In the second hour 25 % more people purchased admission tickets than the first hour . Each ticket cost 15.25 . What was the total amount of money paid for all the tickets purchased in the first two hours please help

Help!!! Please help me I need help on my homework!​

What is the value of the expression?
2 x[(-6 + 4) X (5 + 9) - 3]

Gloria sells skateboards and charges a $15 shipping fee for each skateboard. She sold 14 skateboards last week and charged a total of $938. If Gloria charges the same amount for each skateboard, how much does she charge for one skateboard?

Which function is the best represented by the graph?​

the product of lisa and her twin brother is 36 and their sum is 36 how old can lisa be

HELP ASAP GIVING BRAINLIEST!!!

Beginning with a regular hexagon, a 6-pointed star is formed by constructing equilateral triangles, whose sides are the same length as the sides of the hexagon, on each side of the hexagon as shown. One of the equilateral triangles is shaded. The shaded area is what fractional part of the entire area of the 6-pointed star? Express the answer as a fraction in simplest form.

Question number 3 please will give brainliest if correct.

Hi it ravens home 1
Student’s Answer Key Ch.2 Grammar Advantage Eric Nelson & George Yule © 2019 Student’s Answer Key, Chapter 2, Sentence structure, Grammar Advantage
For most exercises, this key does not include even-numbered items.
■ Exercise 1 Read the passage. Based on what you already know, underline the verbs.
The Marshmallow Experiment
Imagine that you are seven years old. You are participating in an experiment. A researcher greets you and shows you into a small room. In the room there is a marshmallow. The marshmallow is for you, but here is the interesting part: The researcher tells you that he is going to leave you alone in the room for a while. You can eat the marshmallow right away, or you can wait until he gets back. If you wait until he gets back, you will get a second marshmallow.
What do you do? Do you eat the marshmallow right away?
An experiment like this, known informally as the marshmallow experiment, was conducted decades ago at Stanford University. It turned out that some children ate the marshmallow right away, while others were able to wait. In other words, some sought instant self-gratification, and some delayed it.
Years later, the researchers followed up on the participants. They found that the children who delayed self-gratification were in general more successful than those who ate the marshmallow right away. By a variety of measures, including SAT scores, they appeared to be more competent.
Common sense tells us that the ability to delay self-gratification is a mark of maturity. The marshmallow experiment provides evidence that it may also correlate with success in life.
Notes:
- Many of these verb phrases consist of an auxiliary verb and a main verb. So, for example, “are participating” and “do...eat” are considered verb phrases.
- “is going to leave”: If we consder “is going to” a kind of auxiliary verb, then this is a verb phrase, just like “will leave.”
- “known as...”: If you underlined “known,” that’s fine. It is a verb. It is a nonfinite verb, unlike the other underlined verbs and verb phrases. (See Chapter 4.)
■ Exercise 2 Underline the complete subjects in the sentences below, and double- underline the verbs that go with them. Identifying the subject means identifying the main word of the subject and the parts that modify it. (In the first sentence, the main word is in boldface.) When you underline the verb, include both auxiliary verbs and main verbs (as in the first sentence, with was...used).
In the 1960s and 70s, the term “generation gap” was often used to refer to the differences between young people in the U.S. and their parents’ generation. Many young people felt distant from their parents because of differences in ideas about politics, social issues, and popular culture. Since then, conflicts between generations have diminished in many ways. Child-rearing experts in the late 20th century encouraged parents to be like friends to their children. Thanks to technology, young people and their parents are able to contact each other easily at any time. On any college campus, the students you see texting or talking on cell phones are often communicating with Mom or Dad. Fifty years ago, closeness of this kind was less

If the measure of one interior angle on a regular polygon is 150°, how many sides does the polygon have?

A hot air balloon travels at a constant rate of 3 miles per hour. If the balloon traveled a total of 72 miles, how many hours would it take?

IF answered right i will give brainiest plsssssssssssssss help

Homework #74
W
2. A tour group has $784 to spend on
tickets. If each ticket costs $7, how many
tickets will the group be able to buy?

what is the actual length?

Dane needs to cut 4 strips of border for his rectangular project board. The project board has a length of 12 1/2 inches and a width of 6 1/4 inches. How much border will Dane have left if the border comes in a 60-inch roll?

Please help and please I need help:)

what is the slope formula?


NEED HELP PLZ

Answer these two to get 20 points!!

Find the solution to the system by graphing

Evaluate 2x+3 when x = 1

Joyville has a population of 20,750 people.
Its population is increasing at a rate of 2.7%
each year?

please help me i need it

Parallel/perpendicular definition

pq=3-a√x
make x the subject