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
Sav [38]
1 year ago
9

Please help me with this problem I keep getting this wrong an my son is not understanding clearly.Use the parabola tool to graph

the quadratic function. f(x)=3x^2 + 6x − 24 Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Mathematics
1 answer:
Rina8888 [55]1 year ago
8 0
Explanation

The general vertex-equation of a parabola has the following form:

f(x)=a\cdot(x-h)^2+k.

Where:

• a is a multiplicative factor,

,

• (h, k) are the coordinates of the vertex of the parabola.

In this exercise we have the following equation:

f(x)=3\cdot x^2+6x-24.

Vertex of the parabola

To find the vertex of the parabola, we will complete squares to take the equation f(x) to the general form as in the equation above.

i. We factorize the equation of f(x) in the following way:

f(x)=3\cdot(x^2+2x)-24.

ii. Now, we rewrite the term inside the parenthesis as:

\begin{gathered} f(x)=3\cdot(x^2+2\cdot1\cdot x)-24 \\ =3\cdot((x^2+2\cdot1\cdot x+1)-1)-24 \\ =3\cdot(x^2+2x+1)-3-24 \\ =3\cdot(x^2+2x+1)-27. \end{gathered}

iii. Now, we see that the term in parenthesis can be rewritten as a square:

f(x)=3\cdot(x+1)^2-27.

iv. Finally, we rewrite the term inside and outside the parenthesis as:

f(x)=3\cdot(x-(-1))^2+(-27).

In the last step, we rewrite the term inside the parenthesis to have the same shape as in the general expression.

Comparing the equation that we have obtained and the general one, we see that the coordinates of the vertex are:

(h,k)=(-1,-27).

Second point

We find a second point by evaluating the function f(x) in x = 1, we get:

f(1)=3\cdot1^2+6\cdot1-24=3+6-24=-15.

The coordinates of the second point are (1, -15).

Graph

We have the following points of the parabola:

\begin{gathered} \text{ Vertex }=(-1,-27), \\ \text{ Second point }=(1,-15). \end{gathered}

Using these points and taking into account that the axis of symmetry is x = -1 (because the x-coordinate of the vertex is -1), we get the following graph:

Answer

Coordinates of the vertex: (-1, -27)

Coordinates of the second point: (1, -15)

You might be interested in
Paul bought a photo frame which measured 10 inches in length and 8 inches in width. Determine the diagonal length of the photo f
Katyanochek1 [597]

Answer:

≈12.8

Step-by-step explanation:

hope this helps

7 0
2 years ago
Read 2 more answers
Please Help Me:!!!!!
butalik [34]

Answer:

Vertical stretch of factor of 3

translated to the right 2

translated up 5

Step-by-step explanation:

6 0
3 years ago
How to do slope intercept form again?!
Anestetic [448]
You intercept by shaping in a volcano form if that's what you mean
8 0
3 years ago
WILL MARK BRAINLIEST!!
bija089 [108]

Answer:

3 rd one

Step-by-step explanation:

Please mark me as brainliest, vote 5.0 and thank me to support

3 0
3 years ago
Read 2 more answers
The equation x^2+ (k - 3)x + (3 - 2k) = 0, where k is a constant, has two distinct real roots.
Lisa [10]

Step-by-step explanation:

For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,

b^2 - 4ac must be positive.

b^2 - 4ac > 0

(k - 3)^2 - 4(3 - 2k) > 0

k^2 - 6k + 9 - 12 + 8k > 0

k^2 + 2k - 3 > 0

4 0
2 years ago
Other questions:
  • Which statement is correct regarding the measurements of the parallelogram?
    6·2 answers
  • Which statements are true about the graph of the function f(x) = 6x – 4 + x2?
    5·1 answer
  • 8 - ( 3 + b ) = b - 9<br> b = ?
    12·2 answers
  • Mathematics (Reasked) Thank you for any answers, please be sure of it before you respond.
    7·1 answer
  • I need help number 2 and number 4
    14·1 answer
  • You are throwing darts at a dart board. You have a 1/ 6 chance of striking the bull's-eye each time you throw. If you throw 3 ti
    13·2 answers
  • Last question and im not sure how to solve it?? pls help
    9·1 answer
  • Why is it important to take personal responsibility for becoming<br> financially literate?
    15·1 answer
  • Jaques journal is 300 pages long he use 10% of the pages in his journal
    10·1 answer
  • Your school wants to test the fire alarm system during the two hour period between 9:00 a.M. And 11:00 a.M. The probability of t
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!