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
Nuetrik [128]
3 years ago
13

What are the key aspects of the graph of f(x) = x2 - 62, where b is a real number?

Mathematics
1 answer:
8090 [49]3 years ago
7 0

Answer:

The x intercepts are b , - b

The y-intercept is - b²

The vertex is (0 , - b²)

The axis of symmetry of the function is the y-axis

Step-by-step explanation:

* Lets explain the key aspects of the quadratic function

- There are many key aspects in a quadratic graph such as:

# x-intercepts

# y-intercept

# The vertex

# Axis of symmetry

* Lets solve the problem

∵ f(x) = x² - b² is a quadratic function

∵ The general form of the quadratic function is f(x) = Ax² + B(x) + C

   where A , B , C are constant

∴ A = 1 , B = 0 , C = -b²

- To find the x-intercept put f(x) = 0

∵ f(x) = x² - b²

∴ x² - b² = 0 ⇒ add b² for both sides

∴ x² = b² ⇒ take √ for both sides

∴ x = ± b

∴ The x intercepts are b , - b

- To find the y-intercept put x = 0

∵ f(x) = x² - b²

∴ f(0) = 0 - b²

∴ f(0) = - b²

∴ The y-intercept is - b²

- The vertex of the function is (h , k) where h = -B/2A and k = f(h)

∵ A = 1 and B = 0

∴ h = 0/2(1) = 0

∵ k = f(h)

∴ k = f(0) = 0 - b² = - b²

∴ k = - b²

∴ The vertex is (0 , - b²)

- The axis of symmetry of the quadratic function is a vertical line

  passes through the vertex of it and its equation is x = h

∵ h = 0

∴ The equation of the axis of symmetry is x = 0

∵ The equation of the y-axis is x = 0

∴ The axis of symmetry of the function is the y-axis

You might be interested in
PLEASE HELP. WILL GIVE BRAINIEST AND 60 POINTS if you show work so I can understand these.
Greeley [361]

Answer:

In #1, the slope of the line is 3

Step-by-step explanation:

To find the slope of any line, you need to use the points in the slope formula.

m(slope) = (y2 - y1)/(x2 - x1)

m = (5 - 2)/(0 - -1)

m = 3/1

m = 3

This means the slope is equal to 3.

5 0
3 years ago
What is the greatest common factor (GCF) of 48 and 56? A. 168 B. 8 C. 4 D. 336
Sergio039 [100]

Answer:

B. 8

Step-by-step explanation:

48/8=6

56/8=7

7 0
3 years ago
Read 2 more answers
SOLUTION: y = 5x + 7 what is the value of y
Nat2105 [25]
There are an infinite number of solutions given the information you provided. For every real value of x there will be a corresponding real value of y.

y=5x+7  Has not restriction upon the domain or range...

What is the value of y?  5x+7 
8 0
3 years ago
Read 2 more answers
The average amount of rent paid for apartments in Campbell is $1,331, which is 10% more than it was last spring. What was the av
baherus [9]

Answer:

1197.9

Step-by-step explanation:

10 percent of 1331 is 133.1.

because its 10 percent more, you need to do 1331-133.1:)

4 0
3 years ago
State whether or not the following triangles are similar. If not, explain why not. If so, write a similarity statement
valentinak56 [21]

9514 1404 393

Answer:

  a) ∆RLG ~ ∆NCP; SF: 3/2 (smaller to larger)

  b) no; different angles

Step-by-step explanation:

a) The triangles will be similar if their angles are congruent. The scale factor will be the ratio of any side to its corresponding side.

The third angle in ∆RLG is 180° -79° -67° = 34°. So, the two angles 34° and 67° in ∆RLG match the corresponding angles in ∆NCP. The triangles are similar by the AA postulate.

Working clockwise around each figure, the sequence of angles from lower left is 34°, 79°, 67°. So, we can write the similarity statement by naming the vertices in the same order: ∆RLG ~ ∆NCP.

The scale factor relating the second triangle to the first is ...

  NC/RL = 45/30 = 3/2

__

b) In order for the angles of one triangle to be congruent to the angles of the other triangle, at least one member of a list of two of the angles must match for the two triangles. Neither of the numbers 57°, 85° match either of the numbers 38°, 54°, so we know the two triangles have different angle measures. They cannot be similar.

7 0
3 years ago
Other questions:
  • You own two vehicles. a car
    15·1 answer
  • What is a nonlinear function
    5·2 answers
  • Can someone help me real quick?
    15·1 answer
  • How are the areas of two similar figures related
    13·1 answer
  • The formula h=40 +50t+10t2 can be used to find the height h, in meters, of an object shot upward from the top of a 40 meter
    12·1 answer
  • What number should be placed in the box to help complete the division calculation?
    8·2 answers
  • 0.5x = -0.87x + 0.37x<br> Show me the work
    5·1 answer
  • Which expressions are equivalent to 2(2x + 4y + x − 2y)?
    11·1 answer
  • A quiz had 20 questions. Andre scored 16 of them correctly. What was<br> Andre's percent score? *
    8·2 answers
  • Unit #3 Lesson #4 Exit Ticket: The function y=h(x) is shown graphed below. Answer the following questions based on the graph.​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!