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bazaltina [42]
2 years ago
14

Which of the following statements are true about the graph. check all that apply?

Mathematics
1 answer:
oee [108]2 years ago
8 0

Answer:

Statement 1

The graph has a minimum.

This statement is true. The graph has a minimum at x = -1 that is f(-1) = -9.

Statement 2

The graph has a maximum.

The statement is false. As there is no downward curve nor a rigid endpoint but the graph is continuous in upward direction.

Statement 3

The graph has zeros of -4 and 2.

The statement is true because f(-4) = 0 and f(2) = 0.

Statement 4

The vertex is located at (-1, -9).

The statement is true as apparent in the graph.

Statement 5

The solution of the quadratic function represented by the graph is (-1, -9).

The statement is false. Solution of the graph is at the point where f(x) becomes zero. At (-1,-9), f(x) = -9. Hence solution is not at point (-1,-9).

Statement 6

The y-intercept of the graph is (0, -8).

The statement is true. y-intercept of a graph is where the graph intercept the y-axis which means x = 0. As x = 0 at (0, -8), it is the y-intercept of the graph.

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Points S, L, and P on this grid represent the locations of the school, the library, and the park, respectively.
agasfer [191]

Using the distance formula, the distance from:

School to Library (SL) = 5 units.

Library to Park (LP) = 10 units.

<h3>What is the Distance Formula?</h3>

To calculate the distance between two points on a coordinate plane, the distance formula used is: d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}.

Given the coordinates of each location as:

  • School, S = (0, 4)
  • Library, L = (4, 1)
  • Park, P = (-4, -5)

Distance from School to Library (SL):

SL = √[(4−0)² + (1−4)²]

SL = √[(4)² + (−3)²]

SL = √25

SL = 5 units

Distance from Library to Park (LP):

LP = √[(4−(−4))² + (1−(−5))²]

LP = √[(8)² + (6)²]

LP = √100

LP = 10 units

Learn more about the distance formula on:

brainly.com/question/661229

#SPJ1

7 0
1 year ago
What is the expected value of the above spinner?
vova2212 [387]

A spinner, is divided in half, vertically. The right side, is labeled For the spinner below, calculate the expected value. Answer: 1 4 ( − 3 ) + 1 4 ( 10 ) ...
4 0
3 years ago
I need help please help
Bumek [7]

Answer:

:) good day mate

Step-by-step explanation:

:) indeed

6 0
3 years ago
Carl Brownstein is a golf course groundkeeper whose annual gross pay is $45,500. He has exemptions of $3,000. The tax state on t
zhenek [66]

Answer:

Step-by-step explanation:

7 0
3 years ago
Graph the following three equations on your own device and answer the questions below.
Alina [70]

Due to length restrictions, we kindly invite to read the explanation of this question for further details on functions.

<h3>What are the characteristics of each of the three functions?</h3>

a) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(10) = 5 · 10 + 7

f(10) = 57

Case 2

f(10) = 10² + 6

f(10) = 106

Case 3

f(10) = 2¹⁰ + 3

f(10) = 1027

b) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(100) = 5 · 100 + 7

f(100) = 507

Case 2

f(100) = 100² + 6

f(100) = 10006

Case 3

f(100) = 2¹⁰⁰ + 3

f(100) = 1.267 × 10³⁰ + 3

c) In this part we must evaluate each of the three functions at the given value of x:

Case 1

f(1000) = 5 · 1000 + 7

f(1000) = 5007

Case 2

f(1000) = 1000² + 6

f(1000) = 1000006

Case 3

f(1000) = 2¹⁰⁰⁰ + 3

f(1000) = (1.268 × 10³⁰)¹⁰ + 3

f(1000) = 10.744 × 10³⁰⁰ + 3

f(1000) = 1.074 × 10³⁰¹ + 3

e) The <em>third</em> function increases the fastest.

f) In this part we need to compare the <em>third</em> function with respect to the <em>first</em> and <em>second</em> functions:

5 · x + 7 = 2ˣ + 3

2ˣ - 5 · x   = 4

The solutions of the equation are x = - 0.675 and x = 4.81. The function will exceed the other <em>first</em> function at x = 4.81.

x² + 6 = 2ˣ + 3

2ˣ - x² = 3

The solution of the equation is x = 4.588. The function will exceed the other <em>second</em> function at x = 4.588.

g) Yes, <em>exponential</em> functions with bases greater than 1 will surpass <em>polynomic</em> function at any point x such that x > 0.

h) The domain represents the set of x-values of a function and the range represents the set of y-values of a function. Then, the domain and range of each function is:

Case 1

Domain - All <em>real</em> numbers.

Range - All <em>real</em> numbers

Case 2

Domain - All <em>real</em> numbers.

Range - [6, +∞)

Case 3

Domain - All <em>real</em> numbers.

Range - (3, +∞)

To learn more on functions: brainly.com/question/12431044

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5 0
1 year ago
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