Answer:
please give me brilliant answer
Boundless Algebra
Quadratic Functions and Factoring
Graphs of Quadratic Functions
Parts of a Parabola
The graph of a quadratic function is a parabola, and its parts provide valuable information about the function.
LEARNING OBJECTIVES
Describe the parts and features of parabolas
KEY TAKEAWAYS
Key Points
The graph of a quadratic function is a U-shaped curve called a parabola.
The sign on the coefficient aa of the quadratic function affects whether the graph opens up or down. If a<0a<0, the graph makes a frown (opens down) and if a>0a>0 then the graph makes a smile (opens up).
The extreme point ( maximum or minimum ) of a parabola is called the vertex, and the axis of symmetry is a vertical line that passes through the vertex.
The x-intercepts are the points at which the parabola crosses the x-axis. If they exist, the x-intercepts represent the zeros, or roots, of the quadratic function.
Key Terms
vertex: The point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function.
axis of symmetry: A vertical line drawn through the vertex of a parabola around which the parabola is symmetric.
zeros: In a given function, the values of xx at which y=0y=0, also called roots.
Recall that a quadratic function has the form
f(x)=ax2+bx+cf(x)=ax2+bx+c.
where aa, bb, and cc are constants, and a≠0a≠0.
The graph of a quadratic function is a U-shaped curve called a parabola. This shape is shown below.

Parabola : The graph of a quadratic function is a parabola.
In graphs of quadratic functions, the sign on the coefficient aa affects whether the graph opens up or down. If a<0a<0, the graph makes a frown (opens down) and if a>0a>0 then the graph makes a smile (opens up). This is shown below.

Direction of Parabolas: The sign on the coefficient aa determines the direction of the parabola.
Features of Parabolas
Parabolas have several recognizable features that characterize their shape and placement on the Cartesian plane.
Vertex
One important feature of the parabola is that it has an extreme point, called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph.
Axis of Symmetry
Parabolas also have an axis of symmetry, which is parallel to the y-axis. The axis of symmetry is a vertical line drawn through the vertex.
yy-intercept
The y-intercept is the point at which the parabola crosses the y-axis. There cannot be more than one such point, for the graph of a quadratic function. If there were, the curve would not be a function, as there would be two yy values for one xx value, at zero.
xx-intercepts
The x-intercepts are the points at which the parabola crosses the x-axis. If they exist, the x-intercepts represent the zeros, or roots, of the quadratic function, the values of xx at which y=0y=0. There may be zero, one, or two xx-intercepts. The number of xx-intercepts varies depending upon the location of the graph (see the diagram below).

Possible xx-intercepts: A parabola can have no x-intercepts, one x-intercept, or two x-intercepts
Recall that if the quadratic function is set equal to zero, then the result is a quadratic equation. The solutions to the equation are called the roots of the function. These are the same roots that are observable as the xx-intercepts of the parabola.
Notice that, for parabolas with two xx-intercepts, the vertex always falls between the roots. Due to the fact that parabolas are symmetric, the
What is the area of the rhombus shown below?
Answer:
54
Step-by-step explanation:
12*9/2=108/2=54mm^2
Let A = {a, b, c, d}, B = {a, c, d, e}. Let f : A → R and g : B → R such that f = {(a, 1),(b, 2),(c, 2),(d, 4)} and g = {(a, 0),(c, 4),(d, 8),(e, 0)}. State the domain and find: f/g
Answers:
Domain = {c, d}f/g = { (c, 1/2), (d, 1/2) }============================================================
Explanation:
The domain of f: {a,b,c,d} which is drawn from set A.
The domain of g: {a,c,d,e} which is drawn from set B
So far, we can see the possible inputs are: a,b,c,d,e
Let's go through each lowercase letter of the given sets
If 'a' is plugged into f/g, then we'll have 0 in the denominator due to the ordered pair (a,0) in function g. This causes a division by zero error so the input 'a' is not allowed in the domain of f/g.If we tried b, then it would work for function f, but it doesn't work for function g. If we tried to compute g(b), then the result is undefined. This is because the lowercase b input is not found in set uppercase B which is where function g selects its inputs from. So b is eliminated.The input c does work however. f(c) = 2 because of the ordered pair (c,2) in the function f. Similarly, g(c) = 4. This means f/g = 2/4 = 1/2 when the input is c. This shows that c is a valid input in the domain of f/g.The input d is pretty much the same story as input c. Moreover, the input d leads to the same output as c does. This time we have f/g = 4/8 = 1/2 when the input is d. Therefore, d is another valid input in the domain of f/g.The input e is not valid because (e,0) will lead to a division by zero error, as it's part of the g(x) function. So we must eliminate 'e' as a valid option in the domain. Even if we didn't have a division by zero error, we still have the fact that 'e' is not in the domain of the first function f. This is another reason why f/g is not defined when the input is 'e'.To summarize, only inputs c and d are valid in the domain.
The domain is the set {c, d}
Both inputs in the domain lead to the output 1/2. This means the range of f/g is {1/2}. Despite having just one element inside, we must use curly braces to indicate we have a set.
The function f/g is { (c, 1/2), (d, 1/2) }
We simply list all of the (x,y) ordered pairs to describe the function. In this case, there are only two such pairs.
Pls help will do brainliest answer
Answer:
[tex]f(x) = 15 \csc(x) + 5[/tex] (first option)
Step-by-step explanation:
[tex]f(x) = a \: \csc(x) + b[/tex]
[tex]a + b = 20[/tex]
[tex] - a + b = - 10[/tex]
••••
[tex]2b = 10[/tex]
[tex]b = 5[/tex]
[tex]a = 20 - 6 = 15[/tex]
[tex] = f(x) = 15 \csc(x) + 5[/tex]
Classify the following polynomials. Combine like terms first. PLEASE ANSWER I'm really confused. :(
2x-x2+4x+x2
x3-5x2+3-2
x3-x3+x2-x2+3
7x-x2+x3+4x2
-6x-x3+6x-4x
Quadratic monomial
Quadratic binomial
Quadratic trinomial
Cubic monomial
Cubic binomial
Cubic trinomial
Linear monomial
Constant monomial
5−33−32+39+3
Not sure?
6. (09.02 MC)
An object's velocity is defined by the vector-valued function v(t)
= (In(t –2), e^(2t-t^2))
What is the acceleration vector a(t) at t(3)? (10 points)
O
01-14
O
O
Answer:
Hello,
Step-by-step explanation:
[tex]v_x(t)=ln(t-2)\ \Longrightarrow\ a_x(t)=\dfrac{1}{t-2} \\\\v_y(t)=e^{2t-t^2}\ \Longrightarrow\ a_y(t)=e^{2t-t^2}*(2-2t)\\\\t=3\ i\ suppose\ \\\\a_x(3)=\dfrac{1}{3-2}=1\\\\a_y(t)=e^{6-9}*(2-6)=-\dfrac{4}{e^3}[/tex]
Is 1 3/4 closer to 1 or 2 ? Explain your answer
Answer:
it's closer to 2
Step-by-step explanation:
In order to get to 1 from that number, you have to subtract 3/4. In order to get to 2 from that number, you only have to add 1/4. Clearly, the jump in adding is smaller than the jump to subtracting, which means it's closer to 2.
The number is closer to 2
What is fraction?A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fractio" which means 'to break'. The Egyptians, being the earliest civilization to study fractions, used fractions to resolve their mathematical problems, which included the division of food, supplies, and the absence of a bullion currency.
All fractions consist of a numerator and a denominator and they are separated by a horizontal bar known as the fractional bar.
The denominator indicates the number of parts in which the whole has been divided into. It is placed in the lower part of the fraction below the fractional bar.The numerator indicates how many sections of the fraction are represented or selected. It is placed in the upper part of the fraction above the fractional bar.Given number:
1 3/4 = 7/4
On dividing
7/4 = 1.75
Hence, the number is closer to 2.
Learn more about fraction here:
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Find the missing side, then, round to the nearest tenth.
Looking for help with this problem!
Answer:
4.6 = x the side opposite C would be 6.1
Step-by-step explanation:
you can use law of sine
you know you have a right triangle so the missing angle B = 49
4/sin41=x/sin49
For what values of k will the equation 4x² + 8x + k = 0 have two complex solutions?
Answer:
k = -4x² - 8x
Step-by-step explanation:
Subtract 4x² from both sides of the equation.
8x + k = -4x²
Subtract 8x from both sides of the equation.
k = -4x² - 8x
Answer:
k > 4
Step-by-step explanation:
Using the discriminant to determine the nature of the solutions
• If b² - 4ac < 0 then the solutions are not real, that is they are complex
Given
4x² + 8x + k = 0
with a = 4, b = 8, c = k , then
8² - (4 × 4 × k) < 0
64 - 16k < 0 ( subtract 64 from both sides )
- 16k < - 64
Divide both sides by - 16, reversing the symbol as a result of dividing by a negative quantity.
k > 4
Any value of k greater than 4 will mean the equation has 2 complex solutions
Find the midpoint between each pair of points (-1,-5) and (-5,9)
Answer:
(-3,2) is the midpoint
Step-by-step explanation:
ok
5. (09.06 MC)
The graphs of the polar curves r = sin e-2 and r = cos(20 + 3) are shown.
Find the area of R, which is the region inside r = sin 6-2, but outside r = cos(20 + 3). (10 points)
31.416
12.566
15.708
0 25.133
Answer:
12.566
Step-by-step explanation:
A = ∫1/2(r)^2dtheta from a - b = 0 to 2π
∫1/2(sin^2theta-4sintheta+4)dtheta
[9/4theta+2costheta-1/8sin2theta] from 0 to 2π…
when you solve this you get 14.137 without taking out the cos(2theta+3)
How do you model a decimal using a fraction?
Answer:
The only reason I can’t type it right now it’s cause I’m doing something important so I’m so sorry if I hade to type this out but I’m a bit busy right now And I’m trying to answer as much questions as possible. Thank you
Step-by-step explanation:
Hope this helps you
Write down the decimal in fractions with the denominator 1.
We multiply the denominator and numerator by 10 for every number after the decimal point.
Simplify the fraction if needed.
Question 5
1 pts
Find the coordinate of the other endpoint if the midpoint is (5,5) and endpoint is (-1,4).
O (9,6)
(11,6)
(11, 14)
O (9, 14)
Answer:
(11,6)
Step-by-step explanation:
5x-9=2x+12
can somebody answer this and if possible, can you show work?
Answer:
X = 7
Step-by-step explanation:
5x-9=2x+12
5x-2x=12+9
3x=21
X=21/3
X=7
5. Tristan wants to build a square garden in his backyard that will cover an area of 75 ft². If Tristan has 32 feet of material for the perimeter of the garden, does he have enough? Explain.
Lets find side
Area=75ft^2[tex]\\ \sf\longmapsto Area=(side)^2[/tex]
[tex]\\ \sf\longmapsto (side)^2=75[/tex]
[tex]\\ \sf\longmapsto side=8.3ft[/tex]
Perimeter
[tex]\\ \sf\longmapsto 4(side)[/tex]
[tex]\\ \sf\longmapsto 4(8.3)[/tex]
[tex]\\ \sf\longmapsto 33.2[/tex]
He has 1.2ft short materialSee attachment for the question
Answer:
-22
Step-by-step explanation:
f(x) = 3x^2 - 5
let x= 3
f(3) = 3*(3)^2 -5 = 3(9) -5 =27-5 =22
g(x) = -2x+5
Let x = 3
g(3) = -2(3) +5 = -6+5 = -1
f(3) *g(3) = 22(-1) = -22
Plsssssssssssssssss help fast
Answer:
yes tht right pls mark me branilest
-8 + 2x + 17 - x + 20
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! NOT A MULTIPLE CHOICE!!!
The point (-2, 5) is reflected over an axis and the new point is located in Quadrant 3.
a. Describe the reflection that happened. What axis was the point reflected over?
b. What are the coordinates of the new point?
9514 1404 393
Answer:
x-axis(-2, -5)Step-by-step explanation:
a) The original point is in quadrant 2. Reflection into quadrant 3 is a reflection over the x-axis.
__
b) Reflection over the x-axis changes the sign of the y-coordinate. The new point is (-2, -5).
Study the figure and find the effort.
Please help...
Answer:
300
Step-by-step explanation:
I hope it will help you.
A single ticket for a journey costs $1.25
25 single tickets can be bought in a book for $27
Lily makes 25 journeys.
How much does Lily save by using a book of tickets?
Show your working.
Answer:
answer i dont know please
how do you put 300,000+10,000+6,000+20+9
Answer:
three hundred thousand plus ten thousand plus six thousand plus twenty plus nine
Step-by-step explanation:
300,000 → three hundred thousand
10,000 → ten thousand
6,000 → six thousand
20 → twenty
9 → nine
+ → plus
Now put everything together.
Best of Luck!
[tex](-1)^{2} + 2^{3} -0^{4}[/tex]
Answer:
9Step-by-step explanation:
[tex](-1)^{2} + 2^{3} -0^{4}[/tex]
[tex] = 1 + 8 - 0[/tex]
= 9 (Ans)
ANSWER QUICK 70 POINTS!!!!!!!!!!!!!!
Identify the property that justifies each step asked about in the answer area below.
Line 1: (9+x)x
Line 2: x(9+x)
Line 3: x(x+9)
Line 1-Line 2-Associative property .
Line 2-Line 3- Distributive property
Solution:-[tex]\\ \rm\longmapsto (9+x)x[/tex]
[tex]\\ \rm\longmapsto x(x+9)[/tex]
[tex]\\ \rm\longmapsto x(9+x)[/tex]
[tex]\\ \rm\longmapsto x^2+9[/tex]
Given the sequence -14, -6, -2, 0, 1, ..., find the recursive formula.
Answer:
C is the answer to your question
Help, been trying for forever
It's A and C.
A because if you multiply the numbers inside square roots , you will get exactly same ans.
C because √75 is 5√3 and if you multiply it with 2 you get 10√3. √50 is 5√2 and if you multiply it with 3 then you get 15√2.
Find the area.
D
36 m
1
180 m
N
37 m
A. 1100 m
B. 1066 m
C. 555 m
D. 338 m
Answer:
Area of triangle = 1/2×base×height
= 1/2×37×30
= 555m²
The area of the triangle with the given parameters is 555 m².
Given that, NE=37 m and height=30 m.
What is the formula to find the area of a triangle?The formula to find the area of a triangle is 1/2×b×h.
Where, b=base and h=height.
Now, Area=1/2×37×30=555 m².
Therefore, the area of the given triangle is 555 m².
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(2x+1)(3x+4)=0
2x+1=0 3x+4=0
Solve for both equations. What are the two x-values/answers going to be? Leave your answer in a simplified fraction.
(I don’t know what to do next)
Answer:
2x+1=0.
2x=0-1.
2x=-1.
2x/2=-1/2.
x=-2.
3x+4=0
3x=0-4
3x=-4
3x/3=-4/3
[tex]x = 1 \frac{1 }{3} [/tex]
THE STUDENTS ON THE SCHOOL NEWSPAPER ARE CONTRIBUTING MONEY FOR A GIFT FOR THEIR STAFF ADVISOR. THE COST PER STUDENT FOR THE GIFT VAIES INVERSELY AS THE NUMBER OF STUDENTS WHO CONTRIBUTE. iT WILL COST $6 PER STUDENT IF 12 STUDENTS CONTRIBUTE. HOW MUCH WILL IT COST PER PERSON IF 15 STUDENTS CONTRIBUTE
Answer:
ok
Step-by-step explanation:
The sides in each pair of figures are proportional. Find the missing length.
Answer:
41. is c.
42. is d.
Step-by-step explanation:
2ja bag has 3 red and 6 green balls. Two
balls are drawn from the bag one after the
other without replacement. What's the
probability of having a green ball drawn
both times
Answer:
5/12
Step-by-step explanation:
Probability of drawing green ball on the first time=6/9=2/3
Probability of drawing green ball on the second time=5/8
Probability of having a green ball drawn
both times=(2/3)*(5/8)=10/24=5/12