1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
slega [8]
2 years ago
8

What are the coordinates of the vertex of the parabola with the equation y = x + 2x - 3?

Mathematics
1 answer:
loris [4]2 years ago
4 0

Answer:

<em>The coordinates of the vertex are (-1,-4).</em>

Step-by-step explanation:

<u>Equation of the Quadratic Function </u>

The vertex form of the quadratic function has the following equation:

y-k=a(x-h)^2

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.

We are given the function:

y=x^2+2x-3

We must transform the equation above by completing squares:

The first two terms can be completed to be the square of a binomial. Recall the identity:

x^2+2xy+y^2=(x+y)^2

Thus if we add and subtract 1:

y=(x^2+2x+1)-3-1

Operating:

y=(x^2+2x+1)-4

The trinomial in parentheses is a perfect square:

y=(x+1)^2-4

Adding 4:

y+4=(x+1)^2

Comparing with the vertex form of the quadratic function, we have the vertex (-1,-4).

The coordinates of the vertex are (-1,-4).

You might be interested in
Petra jogs 3 miles in 30 minutes at this rate how long would it take a jog 10 miles​
bazaltina [42]

Answer:

100 minutes or 1 hour and 40 minutes

Step-by-step explanation:

3 miles in 30 minutes means 1 mile in 10 minutes

10 miles takes 100 minutes or 1 hour and 40 minutes.

7 0
3 years ago
Read 2 more answers
Is the relationship shown by the data linear? If so, model the data with an equation. x y –7 5 –5 9 –3 13 –1 17
diamong [38]

Given:

The table of values is:

x :     -7          -5         -3           -1

y :      5           9         13          17

To find:

Whether the given data is linear and then find the equation.

Solution:

The given data is linear if the slope and rate of change is constant.

Slope formula:

m=\dfrac{y_2-y_1}{x_2-x_1}

Using the slope formula. we get

\dfrac{9-5}{-5-(-7)}=2

\dfrac{13-9}{-3-(-5)}=2

\dfrac{17-13}{-1-(-3)}=2

Since the rate of change is constant, i.e., 2, therefore the given data is linear.

The slope of a linear equation is 2 and it passes through the point (-7,5). So, the equation of the line is:

y-y_1=m(x-x_1)

y-5=2(x-(-7))

y-5=2(x+7)

y-5=2x+14

Adding 5 on both sides, we get

y-5+5=2x+14+5

y=2x+19

Therefore, the equation for the given data is y=2x+19.

8 0
3 years ago
Identify the quadratic term in the function. Please Help!!! ASAP!!!
Goshia [24]
The quadratic term is 2x^2.
7 0
3 years ago
What value of x will make this expression equal to 28.1? A) x=0 is the only value that will make the expression equal to 28.1 B)
Nikolay [14]

Answer:

Any value except -3.44 will make the equation equal to 28.1

Step-by-step explanation:

We are told to multiply the quotient of the fraction by 28.1 to make 28.1. So, it is obvious that the fraction has to simplified to a one. This is possible with any number as whatever the value of x, the numerator and denominator will be equal. But, in the case of -3.44, it will make 5e fraction 0/0, which is undefined and never equal to 1.

I hope this helps

5 0
3 years ago
caroline bought 6 pieces of gold ribbon. each piece was 3/5 of a yard long. How many yards of ribbon did she buy in all?
Zarrin [17]

Answer:

= 3 3/5 yards

Step-by-step explanation:

If 1 piece = 3/5 yard

What about 6 pieces = ?

= (6 x 3/5) ÷ 1

= 18/5 ÷ 1

= 18/5

= 3 3/5 yards

5 0
3 years ago
Other questions:
  • Shanelle already has $137 from babysitting. She needs at least $625 for a new tablet. Which inequality best represents this scen
    13·1 answer
  • Solve the following inequality. Then place the correct answer in the box provided. Answer in terms of a mixed number.
    13·2 answers
  • Whats 4x+-1x equal ?
    7·2 answers
  • Corinne is taking a train into the city. The train travels at a rate of 45 miles per hour. Which quantity depends on the other?
    14·1 answer
  • A circular garden has a diameter of 6 yards what is a area of the garden
    11·1 answer
  • Greg purchased supplies for a party. He had a coupon good for 30% off. He purchased a helium tank rental with an original price
    9·2 answers
  • Given the following exponential function, identify whether the change represents
    13·2 answers
  • Find the values of the variables and the lengths of the sides of the kite.​
    12·1 answer
  • The points (5, -16) and (8, r) lie on a line with slope 4. Find the missing coordinate r.
    15·1 answer
  • Which angle is an adjacent interior angle? <br><br> a. 1<br> b. 2<br> c. 3<br> d. 4
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!