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
n200080 [17]
3 years ago
15

15. Rewrite the given functions in

Mathematics
1 answer:
Lisa [10]3 years ago
4 0

15. The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26

17. The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5

Step-by-step explanation:

Any quadratic function has:

1. A vertex form form f(x) = a(x - h)² + k, where (h , k) are the

   coordinates of its vertex point

2. A standard form g(x) = ax² + bx + c, where a , b , c are constant and

   a is the coefficient of x², b is the coefficient of x and c is the

    y-intercept

3. the x-coordinate of the vertex point h = \frac{-b}{2a} and

    k = f(h)

15.

∵ f(x) = x² + 8x - 10

∴ a = 1 and b = 8

∵ h = \frac{-b}{2a}

∴ h = \frac{-8}{2(1)}=-4

∴ h = -4

∵ k = f(h)

∴ k = f(-4)

- Substitute x by -4 in f(x)

∴ k = (-4)² + 8(-4) - 10

∴ k = 16 - 32 - 10

∴ k = -26

∴ f(x) = (x - -4)² + (-26)

∴ f(x) = (x + 4)² - 26

The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26

17.

∵ g(x) = (x + 3)² - 4

- Lets solve the power 2 of the bracket:

 (1st + 2nd)² = (1st)(1st) + 2(1st)(2nd) + (2nd)(2nd)

∵ (x + 3)² = (x)(x) + 2(x)(3) + (3)(3)

∴ (x + 3)² = x² + 6x + 9

∴ (x + 3)² - 4 = (x² + 6x + 9) - 4

∵ 9 - 4 = 5

∴ (x + 3)² - 4 = x² + 6x + 5

The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5

Learn more:

You can learn more about the vertex form of quadratic function in brainly.com/question/9390381

#LearnwithBrainly

You might be interested in
Suppose A is an invertible n×n matrix and v is an eigenvector of A with associated eigenvalue 4. Convince yourself that v is an
mote1985 [20]

The eigenvector of matrix A4 is 4096.

The eigenvalue of the matrix A-1 is 1/8.

(A+4I) has an eigenvalue of 12.

40 is the eigenvalue of 5Av.

The collection of scalar values known as the eigenvalues of a matrix are connected to the set of linear equations that are most likely contained within the matrix equations.

The eigenvectors are also known as the characteristic roots.

If the matrix A's eigen vector v is linked to an eigen value.

Av then equals lamda v.

The fact that v is an eigen vector of A with the value eight is assumed.

hence, Av = 8v.

We must determine the eigenvalue of A4.

A4*v equals A3(8v) = 84*v equals 4096v.

As a result, the eigenvalue of A4 is 4096.

Suppose A has an eigenvalue of 8. The eigenvalue of A-1 is thus 1/8.

It is calculated that the eigenvalue of (A+4I) is (A +4In)v = Av + 4v = 8v + 4v =12v.

(A+4I) has an eigenvalue of 12.

The value of 5Av's eigenvalue is 5Av = 5*8v = 40v.

40 is the eigenvalue of 5Av.

Learn more about the eigen vectors here:

brainly.com/question/15423383

#SPJ4

7 0
1 year ago
Are these rates equivalent, 96 words typed for 3 minutes; 160 words typed for 5 minutes
monitta
<h2>Greetings</h2>

Answer:

Yes, they are.

Step-by-step explanation:

<h3>1st rate)</h3>

Lets simplify both rates to the rate typer per minute.

(m is minutes)

3m = 96

Divide both sides by 3:

\frac{3m}{3} = \frac{96}{3}

m = 32

So the rate is 32 words per minute.

<h3>2nd rate</h3>

5m = 160

Divide both sides by 5:

\frac{5m}{5} = \frac{160}{5}

m = 32

<h3>So because the rates per minute are the same, they are equivalent.</h3>
<h2>Hope this helps!</h2>
3 0
3 years ago
Which of these is equivalent to x + 1 + x + 2 + x + 3 + x + 4?
butalik [34]

Answer:

what are the options?

8 0
3 years ago
Read 2 more answers
The square root of an integer n is between 9 and 10. What are all the possible values for n. Explain
sashaice [31]
The square root of 9 is \sqrt{81}
The square root of 10 is \sqrt{100}
If \sqrt{n} = 9 to 10
then \sqrt{n} = \sqrt{81} to \sqrt{100}
8 0
3 years ago
0.075 as a fraction
Rudiy27
.075 will be written as 75/1,000. The fraction can then be simplified to the fraction 3/40.
8 0
3 years ago
Read 2 more answers
Other questions:
  • After all costs are split evenly, how much does Max owe Becky? Help please tysm!
    12·2 answers
  • List all the factors of 40
    12·1 answer
  • Plz help!!!!!<br><br> Please!
    13·1 answer
  • Describe the relationship betw
    6·2 answers
  • Question is in the picture
    13·2 answers
  • 10
    13·2 answers
  • Label the sides and name them also explain how you know<br>​
    15·1 answer
  • What would y=-5x+25 look like on a graph? When you find out, please give me an image.​
    15·1 answer
  • WILL GIVE BRAINLY NEED HELP BAD PLZ WUICK <br> What is the perimeter of the triangle?<br> units
    15·1 answer
  • Please help me for urgent<br>​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!