Answers
You can either transform this quadratic equation into a vertex form which would rather painful or use derivatives.
I'll use dervatives. We know that vertex of a quadratic function is either its maxima or its minima, since the leading coefficient [tex]-x^2[/tex] has a negative prefix that means we get a downward turned parabola with minima being the vertex.
First we take the derivative with respect to x,
[tex]\dfrac{d}{dx}-x^2-2x+3=-2x-2[/tex]
The derivative is esentially information what is the slope of a function at a particular x. When the slope is 0 we reached some sort of turning point, such as minima.
We therefore do,
[tex]-2x-2=0\implies x=-1[/tex]
So at [tex]x=-1[/tex] there appears to be a minima or x-coordinate of the vertex of the function.
Plug the coordinate into the function to get y,
[tex]y=f(-1)=-1+2+3=4[/tex]
So the vertex of the function is at [tex]\boxed{(-1,4)}[/tex].
Assuming you don't know derivatives, there is another way.
First compute the roots of the function,
[tex]-x^2-2x+3=0[/tex]
[tex]-(x-1)(x+3)=0[/tex]
[tex]x_1=1,x_2=-3[/tex]
In the middle between [tex]x_1,x_2[/tex] is an x coordinate of a vertex,
[tex]x=\dfrac{x_1+x_2}{2}=\dfrac{1-3}{2}=-1[/tex]
Just like we had before, we compute for y, [tex]h(-1)=4[/tex] and again the result is [tex]\boxed{(-1,4)}[/tex].
Hope this helps :)
Related Questions
what type of number is 4 plus 5 StartRoot 2 EndRoot?
Answers
Step-by-step explanation:
Adding \sqrt{-2}\,\,and\,\,\sqrt{-18}
−2
and
−18
we get 4\sqrt{2i}4
2i
Option C 4 StartRoot 2 EndRoot i is correct.
Step-by-step explanation:
We need to find the sum of: \sqrt{-2}\,\,and\,\,\sqrt{-18}
−2
and
−18
Finding sum:
\sqrt{-2}+\sqrt{-18}
−2
+
−18
\sqrt{-2}
−2
can be written as \sqrt{2}i
2
i
\sqrt{-18}
−18
can be written as \sqrt{18}i
18
i
We know 18 = 2x3x3 = 2x3^2 so,
\sqrt{2i}+\sqrt{2\times 3^2}i
2i
+
2×3
2
i
\sqrt{2i}+3\sqrt{2}i
2i
+3
2
i
Adding like terms:
4\sqrt{2i}4
2i
So, adding \sqrt{-2}\,\,and\,\,\sqrt{-18}
−2
and
−18
we get 4\sqrt{2i}4
2i
Option C 4 StartRoot 2 EndRoot i is correct.
Keywords: Square root
The volume of a cylinder is 64 cubic feet, and the height of the cylinder is 8 feet. What is the radius of the cylinder?
Answers
Answer:
V = pi R^2 * h volume of cylinder (area of base * height)
pi R^2 = 64 / 8 = 8
R^2 = 8 / pi = 2.865
R = 1.69 ft
Resolva a inequação (x + 4)(x – 4) < 0.
Answers
Answer:
-4 < x < 4
Step-by-step explanation:
Can we please have some help
Answers
What is 1 1/2 + 3/16
Answers
Explanation:
1 1/2 + 3/16
= 3/2 + 3/16
= 24/16 + 3/16
= 27/16
age at BBM 2019 Question Group 'A Brief answer questions; 1. Integrate the following: S(ax? + 2bx + c)3/2(2xa + 2b) dx 2.
Answers
If the integral is
[tex]\displaystyle \int (ax^2+2bx+c)^{3/2}(2ax+2b)\,\mathrm dx[/tex]
substitute [tex]u = ax^2+2bx+c[/tex] and [tex]\mathrm du=(2ax+2b)\,\mathrm dx[/tex]. Then you end up with
[tex]\displaystyle \int u^{3/2}\,\mathrm du = \frac25u^{5/2} + C[/tex]
which in terms of x is
[tex]\boxed{\dfrac25(ax^2+2bx+c)^{5/2} + C}[/tex]
WHY DOES NO ONE ANSWER MY QUESTIONS?? Its kinda annoying that i answer others' questions but no one answers mine. Well if anyone feels like helping me heres my question:
A mathematician reported the results from a particular experiment to the researcher who conducted it. The report states that on one specific part of the experiment, a statistical test result yielded a p-value of 0.21. Based on this p-value, what should the researcher conclude?
The test was not statistically significant because 2 × 0.21 = 0.42, which is less than 0.5.
The test was statistically significant because a p-value of 0.21 is greater than a significance level of 0.05.
The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 79% of the time.
The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time.
The test was statistically significant because p = 1 − 0.21 = 0.79, which is greater than a significance level of 0.05.
Answers
Answer:
The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time.
Step-by-step explanation:
This is the right answer,since this result is only observed 21% of the time, so in general it's not significant, so the first 2 are eliminated. The 2 x 0.21 doesn't matter since, the percent is 21% not 42%, so it doesn't even matter. The last question we eliminate is:"The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 79% of the time" 79% of the time is a pretty good amount to say it's significant, but it only says 21% of the time.So, it leaves us with:The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time.
Hope this helps lol (: is this a psat or somethin?
Wyatt translates both lines 6 units
up and 2 units to the left. Which
of the following must be true?
A. After the translation, line f will not
intersect line g.
B. After the translation, line f will be
the same line as g.
C. After the reflection, line f will not
intersect the y-axis.
D. After the reflection, line g will not
intersect the x-axis.
Answers
A translation is a rigid motion, so the shape and length of the figure will not be changed in any way, only the position. C and D can’t be the answer because there was no reflection, only a translation. And it can’t be B because both lines are being translated the same distance.
Find the simple interest principal 8000 rate 12% time 5 1/2 years
Answers
Answer:
5280
Step-by-step explanation:
12% of 8000 = 960
960 x 5.5 = 5280
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
In store A: A box of cotton candy costs 1 dollar, 12 boxes cost 12 dollars. In store B: 12 boxes cost 48 dollars. How much does each box cost in store B?
Answers
Answer:
$4Step-by-step explanation:
To find the cost of each box divide the total cost by the number of boxes:
48/12 = 4In store A:
→ A box of cotton candy cost = $ 1
→ 12 boxes cost = $ 12
In store B:
→ 12 boxes cost = $ 48
Now we have to,
find the cost of each box in the store B.
→ Total cost in B ÷ Total boxes in B
→ 48 ÷ 12 = 4
So, $ 4 is cost of each box in store B.
Phil wants to fence off his rectangular yard. If the yard is 65 feet by 80 feet, and fencing costs $6 per foot, how much will it cost Phil to fence the yard?
Answers
Answer:
Step-by-step explanation:
if Phil intents to surround the entire yard with fence then he needs
6(65)+6(80)870feet of fence >>> this is the parameter of the rectangle
and since the fence cost $6 per foot
total would 870x6= $5220
which of this shape will tessellate?
Answers
Answer: You can consult:
Triangles, squares and hexagons are the only regular shapes which tessellate by themselves. You can have other tessellations of regular shapes if you use more than one type of shape. You can even tessellate pentagons, but they won't be regular ones. Tessellations can be used for tile patterns or in patchwork quilts!
Step-by-step explanation:
I'm not sure but hope it helps.
Two trains leave stations 228 miles apart at the same time and travel toward each other. One train travels at 105 miles per hour while the other travels at 85
miles per hour. How long will it take for the two trains to meet?
Do not do any rounding.
Answers
Answer:
in 20 kilometers round they will meet
The area of a rectangle is 18 m² if the length is 6 m less than five times the width then find the dimensions of the rectangle round off your answer to the nearest hundredth
Answers
Answer:
Step-by-step explanation:
width = w
L = 5w - 6
w(5w - 6) = 18
5w^2 - 6w = 18
5w^2 - 6w - 18 = 0
Using the quadratic equation formula
x = 2.58997 and
x = -1.38997 This root cannot be. (No rectangle has a minus length.
w = 2.58997
L = 5*2.58997 - 6
L = 6.94985
w = 2.59
L = 6.95
1/2. Divided by 2/12 picture
Answers
1/2 divided by 2/12 or 1/6 would be 3.The reciprocal of 1/6 is 6 and multiplied with 1/2 = 3.
Answer:
3
Step-by-step explanation:
[tex] \frac{1}{2} \div \frac{2}{12} [/tex]
➡️ [tex] \frac{1}{2} \times \frac{12}{2} [/tex]
➡️ [tex] \frac{1}{2} \times 6[/tex]
➡️ [tex] = 3[/tex] ✅
Find the arc length of the partial circle. Either enter an exact answer in terms of π or use 3.14 πpi and enter your answer as a decimal
Answers
Answer:
C (circumference) = 2 pi R for circle
A (arc length) = R * theta = pi R = pi * 9 = 28.27
which equation can be used to solve for x in the following diagram?
Answers
Answer:
A
Step-by-step explanation:
We know that it is A because the two smaller angles are being added, and we know the sum is 90 degrees. The only equation that satisfies both of these is A.
Answer:
A
Step-by-step explanation:
because it is a right angled
Determine the volume of
the right rectangular prism
shown.
112 cm
4 cm
24 cm
Answers
Answer:
5376
Step-by-step explanation:
V=sh
Name a pair of addends with a sum of 6?
Answers
Answer:
2 and 4
1 and 5
3 and 3
Step-by-step explanation:
Answer:
1 + 5
2 + 4
3 + 3
I hope I helped out
6 ice cream cones cost $10. How much will 9 cost?
Answers
Answer:
15 dollars
Step-by-step explanation:
We can write a ratio to solve
6 cones 9 cones
------------ = --------------
10 dollars x dollars
Using cross products
6*x = 10 *9
6x = 90
Divide each side by 6
6x/6 = 90/6
x = 15
Solve 6(x - 3) = 11x +7
Answers
Answer:
x = -5Step-by-step explanation:
Given,
6(x-3) = 11x + 7
=> 6x - 18 = 11x + 7
=> 11x - 6x = -18 - 7
=> 5x = -25
[tex] = > x = \frac{ - 25}{5} [/tex]
=> x = -5 (Ans)
[tex]\large\bf{\red{ \bullet}} \: \tt \:\: 6(x - 3) \: = \: 11x + 7[/tex]
[tex]\large\bf{\red{ \bullet}} \: \tt \:\:6x \: - \: 18 \: = \: 11x \: + \: 7[/tex]
[tex]\large\bf{\red{ \bullet}} \: \tt \:\: - 7 \: \: - 18 \: = \: 11x \: - \: 6x[/tex]
[tex]\large\bf{\red{ \bullet}} \: \tt \: \: - 25 \: = \: 5x[/tex]
[tex]\large\bf{\red{ \bullet}} \: \tt \: \cancel\frac{-25}{5} \: = \: x[/tex]
[tex]\large\bf{\red{ \bullet}} \: \tt \: - 5 \: = \: x[/tex]
[tex]\large\bf{\red{ \bullet}} \: \tt \: \: x \: = \: - 5[/tex]
What is this number sentence equal to?
If you could help, thank you so much!
Answers
Answer:
18.63
Step-by-step explanation:
[tex] \frac{6}{10} = 0.6 \\ \frac{3}{100} = 0.03[/tex]
[tex]10 + 8 + 0.6 + 0.03 = 18.63[/tex]
Which of the following tables represent functions? If the relation is not a function, indicate why it is not.
Answers
Step-by-step explanation:
1. the table on the left is a function, with the formula : y = x²
2. the table on the right is also a function, indicated by the values of the input are different each others
Express the limit as a definite integral on the given interval.
n
lim Σ
n→[infinity] n i = 1 [3(xi*)3 − 7xi*]Δx, [2, 5]
Answers
9514 1404 393
Answer:
[tex]\displaystyle\int^5_2 {(3x^3-7x)} \, dx[/tex]
Step-by-step explanation:
The interval of interest becomes the limits of integration. ∆x becomes dx, and the xi are replaced by the variable of integration, x.
Given IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of 15 , the proportion of people with s above 130 is:
Answers
Given the assumption of a normal distribution with a mean of 100 and a standard deviation of 15, a score of 130 represents a z-score of 2. In different mostly older handbooks of descriptive statistics you can find a ‘from z to percentile-table’. Nowadays it’s more easy to use the computer. Using R, a free and open source statistical environment (www.r-project.org), you can use the command pnorm (130, 100, 15) and it will give 0.9772. Because yo want the proportion above that score you use 1-pnorm (130, 100, 15). Another way of writing in R and with for example 3 IQ-scores:
perc = pnorm (c (70, 100, 130), 100, 15)
(1 - perc)
gives you the above-proportion of the IQ-scores of respectively 70, 100 and 130.
6-(-11) how to solve
Answers
Hi ;-)
Calculate
[tex]6-(-11)=6+11=\boxed{17}[/tex]
Answer:
17
Step-by-step explanation:
6-(-11)
Subtracting a negative is like adding
6+11
17
Write the ratio 2/3/4/5 in simplest form
Answers
Answer: The given ratio, in simplest form, is 4/7.
Step-by-step explanation:
Rewrite 2/3.5 as 4/7 by multiplying both the 2 and the 3.5 by 2. This eliminates the decimal fraction.
The given ratio, in simplest form, is 4/7.
Which transformation were used to fcreate traianglemA’ B’ C?
Answers
9514 1404 393
Answer:
(b) dilation by 2, reflection in y-axis
Step-by-step explanation:
Each of the dimensions of ΔA'B'C' is double the corresponding dimension of ΔABC, so dilation by a factor of 2 has occurred.
The sequence of vertices in ΔA'B'C' is CCW, opposite that of ΔABC. Hence, a reflection has taken place. (Rotation keeps the same order.)
The transformation is a dilation by a factor of 2 and a reflection across the y-axis.
Can someone explain this and answer please :)
Answers
Answer:
day 8
Step-by-step explanation:
the rate of change is 2 (x2) which is making the amount saved double each day you can write a formula to represent this sequence:
f(n)=0.01x2^n-1
you put in the day number for n
f(n)=0.01x2^8-1
this gives you 1.28 which is the first day with an amount above 1.00
Please help with my question.
Answers
Answer:
C
Step-by-step explanation:
-4*(-2)=7(r+9)
8=7r+63
-7r=55
r=-55/7=-7 6/7