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
Over [174]
3 years ago
12

A quadratic function is a function of the form y=ax^2+bx+c where a, b, and c are constants. Given any 3 points in the plane, the

re is exactly one quadratic function whose graph contains these points. Find the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17). Enter the equation below. Function: y = 0

Mathematics
1 answer:
pochemuha3 years ago
8 0

Answer:

The quadratic function whose graph contains these points is y=-x^{2}-2x-2

Step-by-step explanation:

We know that a quadratic function is a function of the form y=ax^{2}+bx+c. The first step is use the 3 points given to write 3 equations to find the values of the constants <em>a</em>,<em>b</em>, and <em>c</em>.  

Substitute the points (0,-2), (-5,-17), and (3,-17) into the general form of a quadratic function.

-2=a*0^{2}+b*0+c\\c=-2

-17=a*-5^{2}+b*-5+c\\c=-25a+5b-17

-17=a*3^{2}+b*3+c\\ c=-9a-3b-17

We can solve these system of equations by substitution

  • Substitute c=-9a-3b-17

-9a-3b-17=25a+5b-17\\-9a-3b-17=-2

  • Isolate a for the first equation

-9a-3b-17=-25a+5b-17\\a=\frac{b}{2}

  • Substitute a=\frac{b}{2} into the second equation

-9\left(-\frac{b}{2}\right)-3b-17=-2

  • Find the value of b

-9\left(-\frac{4b}{17}\right)-3b-17=-2\\ b=-2

  • Find the value of a

a=\frac{b}{2}\\  a=-1

The solutions to the system of equations are:

b=-2,a=-1,c=-2

So the quadratic function whose graph contains these points is

y=-x^{2}-2x-2

As you can corroborate with the graph of this function.

You might be interested in
benny bought 8 new basketball trading cards to add to his collection. There are now only 44 cards left.How many cards did benny
Mashcka [7]
<span>So the equation: (x+8) divided by 2 =24</span>
5 0
3 years ago
If one face of a cube has a surface area of 5.25 square meters, what is the surface area of the entire cube
natali 33 [55]

Answer:

11.25

Step-by-step explanation:

if a cube has 6 equal sides, you want to multiply 5.25 by 6 to get the surface area for the entire cube.

6 0
3 years ago
Please answer these I will give you all my points!
makvit [3.9K]
  1. 300
  2. 59
  3. 4
  4. 78

ok so put it like that and it will be correct.............................................................................(long pause)........................................................................................................... (thinks) I think that the right answer.

5 0
3 years ago
Arrange the numbers in increasing order 5.049, 5.069, 5.49, 5.09
s344n2d4d5 [400]

5.049 is the smallest

5.069

5.09

5.49 is the biggest

3 0
3 years ago
Read 2 more answers
Match the pre-image, and its clockwise rotation, with the coordinates of its image.
vladimir2022 [97]

Answer:

<h3>here its simple 0506-5-569756'567o5[76]5567=-5670;675;'6776[5]675</h3>

Step-by-step explanation:

oh and 340450=043=4-re0t4=24--44035054-23=0-65-=302=44934205=-3043504-3=-4-334=-043-40==34=40-[;'30=43-4=053=-=

5 0
3 years ago
Other questions:
  • What is 3 divided into 4 and 1 half
    14·2 answers
  • Find the values of x and y
    15·1 answer
  • Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail inste
    9·1 answer
  • Factor the expression gcf 12w-18
    13·2 answers
  • Which polynomial expression are in standard form
    5·1 answer
  • Which answer choice shows 15.067 rounded to the nearest hundredth?
    6·1 answer
  • A 10-foot ladder is leaning against a wall. The bottom of the ladder is 4 feet from the base of the wall, as shown below.
    15·1 answer
  • The quotient of (x4 + 5x3 – 3x – 15) and a polynomial is (x3 – 3). What is the polynomial?
    9·2 answers
  • 36.95-36.95+59.72?????
    12·2 answers
  • 3x4.-4<br> 5x3 - 2x2<br> 4x3 + 6x<br> ?<br> 4x4 - 2x2 – 3x
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!