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
Aleks04 [339]
3 years ago
13

Identify the​ vertex, the axis of​ symmetry, the maximum or minimum​ value, and the range of the parabola for y=x^2+6x+13

Mathematics
1 answer:
charle [14.2K]3 years ago
4 0

Answer:


Step-by-step explanation:

First we can determine the x value of our vertex via the equation:

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

Note that in general a quadratic equation is such that:

ax^2+bx+c

In this case a,b and c are the coefficients and so a=1, b=6 and c=13.

Therefore we can determine the x component of the vertex by plugging in the values known and so:

x=\frac{-b}{2a}=\frac{-6}{2(1)}=\frac{-6}{2}=-3

Now we can determine the y-component of our vertex by plugging in the x-component to the equation and so:

f(x)=x^2+6x+13\\\\f(-3)=(-3)^2+6(-3)+13\\\\f(-3)=4

Therefore our vertex is (-3,4).  Now in vertex our x component determines is the axis of symmetry so the equation for axis of symmetry is:

x=-3

Similarly, the y-component of our vertex is the minimum or maximum.  In this case it is the minimum you can determine this because a is positive meaning that the parabola will point up, and so the equation for the  minimum is:

y=4

The range of the formula is the smallest y-value meaning the minimum y=4 and all real numbers that are more than 4, mathematically:

Range = All real numbers greater than or equal to 4.

You might be interested in
Enter numbers to write 0.000328
Makovka662 [10]

Answer:

3.28 x 10^-4


Step-by-step explanation:

0.000328 = 3.28 x 10^-4

7 0
3 years ago
A family pass to the amusement park costs $54 Using the Distributive Property,write an expression that can be used to fine the c
ruslelena [56]
<span>The distributive property is: a(b + c) = ab + ac. In this expression, the example would be 8(54 + 0) = (8 x 54) + (8 x 0). The cost of eight family passes is therefore equal to 8 x 54. $432 is the answer.</span>
8 0
2 years ago
A large pizza has 16 slices. You eat 4 pieces and 7 chicken wings. What proportion of the pizza did you eat?
ddd [48]

Answer:

4/16

Step-by-step explanation:

You ate 4 slice of the 16 slice pizza

3 0
3 years ago
Please help. I dont really understand this, you can even just explain it to me and Ill give you brainliest and 30 points :)
polet [3.4K]
When any shape is inscribed in a circle, it means that the shape is within the circle but all of the corners are touching the circle. So this could just look like a square within a circle with the corners of the square touching the circle but not going outside of the borders of the circle. Repeat this process with the other shapes. The central angle used to locate the vertices is found by taking the number of sides on the shape and divide it by 360 (the angle of a circle). So for a square with 4 sides, you would take 360/4 and get 90 degrees. This means that each angle within the square is 90 degrees. That 90 degrees is the interior angle of the polygon (for a square specifically). Then what you do is look at the circle and draw a dot at the center of it. You can use a protractor for this part if you want but you would find the central angle by picking a point on the circle and drawing a line to the center dot, then you rotate however many degrees you found in the interior angle of the polygon and you would draw a new line from the center of the circle to that point. You will continue this process until you have gone back to your starting point on the circle. The amount of times it takes you to repeat the process should be the amount of sides the polygon has that you are trying. Interior angle and central angle should be the same for the individual shapes but it would be different for different shapes like a square and an octagon because there are a different amount of sides.
4 0
3 years ago
I need help in this question
tiny-mole [99]

Answer:

C. 12/15

Step-by-step explanation:

2/3, 6/9, and 18/27 all simplify to 2/3. 12/15 does not.

8 0
2 years ago
Other questions:
  • ⦁ What is 0.36 expressed as a fraction in simplest form? ( there is a line over the 6)
    7·2 answers
  • −px+r=−8x−2 solve for x
    9·2 answers
  • Which of these is an example of a non-random sample?
    8·2 answers
  • A plant grows 3 centimeters in 10 days. How much does it grow per day?
    7·2 answers
  • Evaluate the expression for x=5, y=-3 and z=7<br> 7 - 3y – 3z
    8·2 answers
  • A 5,000 principal is invested into two accounts, one earning 1% and another earning 6% interest. If the total interest for the y
    14·1 answer
  • Remake of steps to graph a line, if equation is 2x+4y=8
    14·1 answer
  • Help me please I'm not sure if im right​
    12·1 answer
  • Jerry solved the system of equations.
    11·1 answer
  • 9th Grade Geometry<br><br> Describe and correct the error in finding the length of line segment AB
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!