Answers
9514 1404 393
Answer:
opening upwardaxis of symmetry: x = 0.25vertex: (0.25, -3.25)x-intercepts: 0.25 ±√0.8125 ≈ {-0.651388, 1.151388}y-intercept: -3Step-by-step explanation:
I find it useful to graph the function using a graphing calculator. That answers most of the questions.
This function is written in standard form (terms have decreasing powers of x). It is a 2nd degree function, because the highest power of x is 2. A second-degree function is also called a quadratic. The leading coefficient is the coefficient of the term with the highest power of x. Here the leading coefficient is 4. The sign of it is positive, which tells you which way the graph opens (when the degree is even).
Opening
When the leading coefficient is positive, the function's graph opens upward. (If it were negative, the graph would open downward.)
Vertex
The vertex is the extreme point on the graph. If you want to find it algebraically, its coordinates are ...
(-b/(2a), c -b^2/(4a))
where 'a', 'b', and 'c' are the coefficients of ax² +bx +c. In this function, a=4, b=-2, c=-3, so the vertex is ...
(-(-2)/(2(4)), -3 -(-2)^2/(4(4))) = (1/4, -3 1/4)
Axis of Symmetry
The axis of symmetry is the vertical line through the vertex. It will have the equation x=constant. Of course, the constant must be the x-value of the vertex (which is why we found the vertex first).
x = 1/4
x-intercepts
The x-intercepts are where the graph crosses the x-axis. The attached graph shows an approximation of them, rounded to thousandths. You can compute the x-intercepts algebraically from the vertex and the leading coefficient.
x-intercepts = (vertex x-value) ± √(-(vertex y-value)/(leading coefficient))
x-intercepts = 1/4 ± √((3 1/4)/(4)) = 0.25 ±√0.8125 ≈ {-0.651388, 1.151388}
y-intercept
The y-intercept is the value of f(0), the point where the graph crosses the y-axis. It is always the constant in the polynomial, named 'c' above. The y-intercept is ...
y-intercept = -3
_____
Additional comment
Sometimes you want the x- and y-intercepts written as coordinates. Of course the y-coordinate of the x-intercepts is 0. Similarly, the x-coordinate of the y-intercept is 0. The coordinate ordered pairs are shown on the graph.
These are fairly standard questions that are asked about quadratic functions. It can be worthwhile to get familiar with the way they are answered. (The computation of the x-intercepts shown here is perhaps a bit unusual, but is very effective once you have the function vertex. The values it gives are correct even when the "x-intercepts" are complex numbers.)
Related Questions
Martin has 128 pencils that he is putting
into boxes. Each box holds 6 pencils. If he
puts all the pencils into boxes, how many
more pencils will he need to fill the last box
completely?
Answers
128 pencils divided by 6 pencils that can be put in a box; 128÷6=21 with a remainder of 3
Martin needs 3 more pencils for the last box, beacuse he has 3 leftovers and 6 can go into the box. 6-3=3
derivative of y=(3x+5)^3
Answers
[tex]\\ \sf\longmapsto \dfrac{dy}{dt}[/tex]
[tex]\\ \sf\longmapsto \dfrac{d}{dt}(3x+5)^3[/tex]
[tex]\\ \sf\longmapsto \{3(3x+5)\}^2[/tex]
[tex]\\ \sf\longmapsto (9x+15)^2[/tex]
[tex]\\ \sf\longmapsto 9x^2+2(9x)(15)+(15)^2[/tex]
[tex]\\ \sf\longmapsto 81x^2+270x+225[/tex]
Step-by-step explanation:
[tex]y=(3x+5)^3\\\\\dfrac{dy}{dx}=\dfrac{d}{dx}(3x+5)^3\\\\\dfrac{dy}{dx}=3(3x+5)^2×\dfrac{d}{dx}(3x+5)\\\\\dfrac{dy}{dx}=3(3x+5)^2×\dfrac{d}{dx}3x+\dfrac{d}{dx}5\\\\\dfrac{dy}{dx}=3(3x+5)^2×3+0\\\\\dfrac{dy}{dx}=9(3x+5)^2\\\\\dfrac{dy}{dx}=9(9x^2+25+30x)\\\\\dfrac{dy}{dx}=81x^2+270x+225[/tex]
I don’t get this type of problem
Answers
Answer:
Which type of problem ...lol u have to mention this too
Answer:
what problem do u have
Step-by-step explanation:
please mark me as brainlest
Please help will mark branliest!!!!
Answers
Answer:
the answer is option B
[tex] {f}^{ - 1} ( \frac{1}{2} x - \frac{3}{2} )[/tex]
f(x)=2+|x-3| for all x than the value of the derivative of x=3 is
Answers
The derivative at x = 3 does not exist.
To see why, recall the definition of absolute value:
[tex]|x| = \begin{cases}x&\text{if }x\ge0\\-x&\text{if }x<0\end{cases}[/tex]
If x - 3 ≥ 0, then
2 + |x - 3| = 2 + (x - 3) = x - 1
and the derivative of this piece is 1 for all x > 3.
If x - 3 < 0, then
2 + |x - 3| = 2 - (x - 3) = 5 - x
and its derivative is -1 for all x < 3.
The derivatives to either side of x = 3 are not the same, so f '(x) is not continuous and indeed does not take on any value at this point.
write the point slope form of: through (1,5), parallel to y=6x
Answers
Answer:
y=6x+10
Step-by-step explanation:
y=6x
y-5=6(x-1)
y-5=6x+5
+5 +5
----------------
y=6x+10
NO LINKS OR ASSESSMENT!
Part 1: State the Domain and Range of each graph in BOTH inequality and interval notation
Answers
Domain:
- 2 < x < 2 or x ∈ (-2, 2)Range:
-3 < y ≤ 5 or y ∈ (-3, 5]#2Domain:
1 ≤ x ≤ 5 or x∈ [1, 5]Range:
-2 < y ≤ 2 or y ∈ (-2, 2]#3Domain:
- 4 < x < 5 or x∈ (-4, 5)Range:
1 < y < 4 or y ∈ (1, 4)Gas mileage is the number of miles you can drive on a a gallon of gasoline. A test of a new car results in 510 miles on 10 gallons of gas. How far could you drive on 40 gallons of gas? What is the car's gas mileage
a. 2040 miles and 51 miles/gallon
b. 2050 miles and 200 miles/ gallon
c. 3040 miles and 50 miles/ gallon
d. 230 miles and 51 miles/gallon
help plis
Answers
Answer:
a. 2040 miles and 51/gallon
Step-by-step explanation:
Help a person out asap plz
Answers
Answer:
m∠1 = 52, m∠2 = 60
Step-by-step explanation:
68 and ∠2 are interior angles. 128 is exterior angle.
Formula : -
Sum of two interior angles = Exterior angle
68 + ∠2 = 128
∠2 = 128 - 68
∠2 = 60
∠1 and 128 are linear pair angles. Sum of linear pair angles is 180,
∠1 + 128 = 180
∠1 = 180 - 128
∠1 = 52
Line segment XY has endpoints X(5,7) and Y(-3,3)
Answers
y=-2x+7
Step-by-step explanation:
line segment xy has endpoints x(5 7) and y(-3 3)
for the equation of the perpendicular bisector of line segment xy
slope of line segment xy = 7-3 / 5+3
= 4/8
=1/2
so slope of perpendicular bisector is -2
as m1m2= -1 or m1= -1/m2
As perpendicular bisector goes through midpoint of xy , let's find midpoint of xy
midpoint(x,y) = (5-3 / 2 , 7+3 / 2)
=(2/2, 10/2)
=(1,5)
find the equation of line(perpendicular bisector) passing through (1,5) and the slope -2
y-5 = -2(x-1)
y-5 =-2x+2
y=-2x+7
What is the solution?
[tex] \lim_{x\to1} \frac{x + 2}{ x + x} [/tex]
Math please
Answers
Answer:
[tex] 1 \frac{1}{2} [/tex]
Step-by-step explanation:
[tex] \lim_{x\to1} \frac{x + 2}{ x + x} [/tex]
[tex] = \frac{1 + 2}{ 1 + 1} [/tex]
[tex] = \frac{3}{2} [/tex]
[tex] = 1 \frac{1}{2} [/tex]
Answer:
1/2
Step-by-step explanation:
Ok, understand?
.......
Find the third degree polynomial function that has an output of 40 when x = 1, and has zeros - 19 and -i?
Answers
Answer:
f(x) = x³ + 19x² + x + 19
Step-by-step explanation:
Zeros: -19 , -i, complex conjugate root: +i
Function: (x+19)(x+i)(x-i) = 0
(x + 19) (x² - i²) = (x + 19) ( x² + 1) = x³ + 19x² + x + 19
check: when x = 1
f(1) = 1 + 19 + 1 +19 = 40
3 unique numbers.
Small to big.
Rotate it upside down, and it
remains the same.
???
¿ ¿
Answers
If you flip it over its still 906
PLS HELP ME undersand THIS
Answers
Answer:
I believe it is answer b.
Step-by-step explanation:
You multiply 4x and - 7 by 1/5 which gives you 4/5x and 1 2/5. You add 4/5x and 2/5x as they are like terms and get 1 1/5x. The equation then becomes 1 1/5 - 1 2/5
if johny had 7 dollars and 45 cents and he got an apple for 3 dollars how much does he have left?
a . 4 dollars
b . 3 dollars
c . 4 dollars 45 cents
d . 3 dollars 45 cents
Answers
Answer:
C. 4 Dollar and 45 cent
Step-by-step explanation:
7.45 subtract 3.00 is 4.45
aka
7.00 subtract 3.00 which is 4.00 and add the 0.45
Answer:
c. I am writing extra stuff to be able to send it lol
Step-by-step explanation:
7 45 - 3 =4. 45
This is the question here
Answers
Answer: 1,200 brainliest plsss
Step-by-step explanation:
HELPPP PLEASEEEE 13% want to be doctors or nurses .
Answers
What does it mean to say two variables are positively associated
Answers
Answer:
A positive correlation is a relationship between two variables in which both variables move in the same direction. Therefore, when one variable increases as the other variable increases, or one variable decreases while the other decreases.
ax^2+bx+c , we get b-c-a=
Answers
Answer:
[tex]0 \: I \: think.[/tex]
5000 x 6 - 70 + 86 divided by 5
First to answer gets brainliest!!!
NO LINKS PLEASE!!!!
Answers
Answer:
30,016
Step-by-step explanation:
Answer: 6003.2
Step-by-step explanation:
HELP ME OUT PLEASE!
A company charges a delivery fee of $50 to deliver plotting soil and each cubic yard of plotting soil costs $50
Based on this information, which graph best shows this relationship between the cost y, and the number of cubic yards, X?
Answers
50:1= 25:0.5
The obtained coordinate points to plot the graph are matching with graph A. Therefore, option A is the correct answer.
Given that, a company charges a delivery fee of $50 to deliver plotting soil and each cubic yard of plotting soil costs $50.
What is graph?In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
Let the total cost be y and the number of cubic yards be x.
Now, the equation to represent the given situation is y = 50+50x
By substituting x = 0, 1, 2, 3, 4, 5,....we get
y = 50+50(0) = 50
y = 50+50(1) = 100
y = 50+50(2) = 150
y = 50+50(3) = 200
y = 50+50(4) = 250
So, the coordinates to plot the graph are (0, 50), (1, 100), (2, 150), (3, 200) and (4, 250) and so on.
The obtained coordinate points to plot the graph are matching with graph A. Therefore, option A is the correct answer.
To learn more about the linear graph visit:
brainly.com/question/28494690.
#SPJ5
2x+3y=24 in slope intercept form
Answers
Answer:
3y = -2x + 24
y = -2/3x + 8
Step-by-step explanation:
Answer:
The slope-intercept form is y=mx+b y = m x + b
Step-by-step explanation:
where m m is the slope and b b is the y-intercept. Subtract 2x 2 x from both sides of the equation. Divide each term by 3 3 and simplify. Divide each term in 3y=24−2x 3 y = 24 - 2 x by 3 3 .
PLZ Will mark brainliest. What are the domain and range of each relation?
Answers
Domain: {-4, -3, 1}
Range: {1, 3, 4}
Hope this was helpful!
Add 2√2 + 5√3 - 7√5 and 3√3 - √2 + √5
Answers
Answer:
this is the answer hope that helps
Write the complete proof in your paper homework and for online (only) respond to questions or statements (if any) that are parts of your proof or related to it.
Prove that the medians to the legs of an isosceles triangle are congruent.
Answer:
What rule did you use to prove triangles congruent? (AAA,SAS,ASA,CannotBeDetermined,SSS)
Answers
Answer:
BD=5, AB=15
Step-by-step explanation:
Because AB = AC, AC =15, SO AB = 15
Because Δ DAB ≅ Δ DAC, So BD = DC =5
Susan is choosing tween two cell phone plans that offer the same amount of free minutes.
Plan A charges $29.99 per month with additional minutes costing $0.45
per minute.
Plan B charghes $39.99 a month with addtional minutes costing $0.40 per minute. If the equation for Plan A is
0.45x + 29.99 and the equation for plan E
is 0.40x+ 39.99, then how many addtional minutes, x, will it take for the two plans to cost the same?
Answers
Answer:
200
Step-by-step explanation:
You can simply just graph it and see where the points intersect, or you can do it algebraically.
0.45x+29.99=0.40x+39.99 subtract 29.99 both sides
0.45x=0.40x+10.00 subtract .40x both sides
0.05x=10.00 divide both sides by 0.05
x=200
Kelly bought a soda for three dollars and 7 candy bars when she went to the movies. She spent a total of $21. How much did each candy bar cost? Write out and solve. Show work
Answers
Answer:
$2.57
Step-by-step explanation:
Create an equation.
7x + 3 = 21
Subtract 3 from both sides of the equation.
7x = 18
Divide 7 from both sides to find x.
18/7 = x,
x = 2.57
Each candy bar costs 2.57 dollars,
Answer:
2.50
Step-by-step explanation
(21-3)/7
PLZ HELP ME ON THIS QUESTION GUYS!!
Answers
a) 3.2a, -4 1/3a, -a
b) -2.133a+6
C. Again, assume that we can't produce more than 1,000 un necessarily some x value, let's call it C, for which the profit is exactly 0? Explain your answer. 2. For the following: A. Produce a function f(x) that satisfies the following conditions: 1. Its domain is all real numbers. 11. It has no maximum and no minimum on the interval (1, 3). III. It satisfies f(1) = 1 and f(3) = -1, but there does not exist a c between 1 and 3 such that f(x) = 0. B. Construct a function f(x) that satisfies the following conditions: C. fis continuous for all x.
Answers
Answer:
C. Yes, there is an x-value that is exactly zero. This is true because zero is our starting point in our profits. The x and y value would be (0,0) as we have just begun to produce energy units. Once the graph starts to increase, we cannot have a point at exactly zero, unless the profits have a dramatic drop to the x value of 0. This would then be (0, at a number of diminishing returns)
Step-by-step explanation:
I am not sure about number two sorry.
3(0.5 - p) - 4(p - 0.75); p = 2
Answers
Answer:
Negative 9.5
Step-by-step explanation:
3(0.5 - 2) - 4(2 - 0.75)
3(-1.5) - 4(1.25)
-4.5 - 5
-9.5