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
docker41 [41]
3 years ago
6

The graph of a quadratic function has roots at -3 and -7 and a vertex at (-5, 4). What is the equation of the function in vertex

form?
Mathematics
1 answer:
melomori [17]3 years ago
3 0

Answer:

y = -(x + 5)² + 4

Step-by-step explanation:

The roots are -3 and -7, so:

y = a (x + 3) (x + 7)

Distribute and complete the square:

y = a (x² + 10x + 21)

y = a (x² + 10x + 25 − 4)

y = a (x² + 10x + 25) − 4a

y = a (x + 5)² − 4a

The vertex is (-5, 4), so a = -1.

y = -(x + 5)² + 4

You might be interested in
In a random sample of 1,000 high-school students, 29 percent indicated that they had read the Declaration of Independence at lea
7nadin3 [17]

Answer:

c. Ninety-five percent of the time, the percentage of those questioned who have read the Declaration of Independence would likely be between 25 and 33 percent.

Step-by-step explanation:

Margin of error:

"It means the percentage difference of the result above or below the exact value."

i.e. 4 percent of margin error in the question means that the result will be either 4 percent above the 29 percent or 4 percent below the 29 percent.

OR "the result can vary upto 4 percent above or below the 29 percent."

Let me simplify the answer first in number then convert it percent to understand easily.

29 percent of 1000=  (29/100)*1000=290

4 percent of 1000=(4/100)*1000=40

If 290 students had read the declaration of independence at least once with 40 margin of error, then it means the number of students that had read declaration of independence may be 330 or 250

250 is 25% of 1000 and 330 is 33% of 1000, that is why ninety-five percent of the time, the percentage of those questioned who have read the Declaration of Independence would likely be between 25 and 33 percent.

4 0
3 years ago
Can I get help with this
Hunter-Best [27]

Answer:

The correct option is;

B) -6

Step-by-step explanation:

The given parameters are;

The line of symmetry of f(x) = The line of the reflection of g(x) over the y-axis

f(x) = 3·x² + b·x + c

From the given graph of g(x), we have;

The vertex point of g(x) = (-1, 8)

The line of symmetry is the line x = -1

The image of the reflection of (x, y) over the y-axis is (-x, y)

The image of the vertex of g(x) following a reflection across the y-axis is (1, 8)

Therefore;

The line of symmetry of the image of g(x) following a reflection over the x-axis is the line x = 1

The line (axis) of symmetry of a quadratic function is the line x = -b/(2·a), which is a line that always go through the vertex of the parabola

Where;

a = The coefficient of x²

b = The coefficient of 'x'

For f(x) = 3·x² + b·x + c, a = 3, and b = b

Given that f(x) and the image of g(x) have the same line of symmetry, we have;

The line of symmetry of f(x) is x = 1

Therefore, from the formula for the line of symmetry, we have;

x = -b/(2·a)

x = 1

By substitution, we have;

1 =  -b/(2·a)

∴ -2·a = b

Given that a = 3, we get;

-2 × 3 = -6 = b

b = -6

3 0
3 years ago
Which shows a correct order to solve this story problem? Each morning Mike bikes 3.5 miles. Each afternoon he bikes 2.3 miles. H
Grace [21]
Ok so
since we h ave
3.5=1 day's morning
and
2.3=1 day's afternoon
we need to add them to find 1 day and multiply by 6 (number of days)
that answer is not listted so we make into anohter form
this wold be
6 times (3.5 +2.3)
if we distributed
a(b+c)=ab+ac
6(3.5+2.3)=6 times 3.5+6 times 2.3

this is D
3 0
3 years ago
Read 2 more answers
(2) (x-7) (=3) (x+8)
Tasya [4]

Use the distributive property to get 2x - 14 = 3x + 24. Subtract 24 from both sides to get 2x - 38 = 3x. Subtract 2x from both sides to get -38 = x.

7 0
2 years ago
Read 2 more answers
Find the value of X.
-Dominant- [34]
To find the value of x we first need to find the missing angle in the triangle.

To do that we are gonna add the angles we already have.

64 + 45 = 109

Angles in a triangle measures 180 so to get the missing angle we are gonna subtract 109 from 180

180 - 109 = 71 deg

The missing angle in the triangle is 71 deg


Angles on a straight line adds up to 10 so to find x we are gonna subtract 71 from 180

180 - 71 = 109 degrees

Therefore x is 109 degrees.
6 0
2 years ago
Other questions:
  • Evaluate :cos 45 by sin 30 + cosec 30​
    13·2 answers
  • Which statement best explains why this expression is equal to 6.27?
    9·2 answers
  • A company manufactures two products. A and B on two machines, I and II. It has been determined that the company will realize a p
    7·1 answer
  • What is the value of g?<br><br>−5+7g=3g+9<br><br>−1<br><br>1<br><br>125<br><br>312
    14·2 answers
  • N^4-11n^2+30/n^4-7n^2+10
    7·1 answer
  • ways to put 72 cookies into an equal amount of bags with more than 2 and less than 10 cookies in each bag
    9·1 answer
  • What is the opposite of 9.2 <br><br><br><br><br> (and don't delete my question!)
    5·2 answers
  • What is the coefficient in the expression 5+ 9y
    11·2 answers
  • What is the y intercept of the graph<br> A. -2<br> B. 2<br> C. -4<br> D. 4
    15·2 answers
  • If anyone can help me :))<br><br> 3n/9n-1
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!