Complete the square to write each equation in vertex form. Then, state whether the vertex is a minimum or a maximum and give its coordinates.
Answers
Answer:
a) y = (x + 1)^2 - 3
b) minimum
c) (-1, -3)
Step by step:
We start with the equation:
y = x^2 + 2*x - 2
First, we want to complete the square to write the equation in the vertex form.
y = (x - h)^2 + k
Such that the vertex is (h, k)
To complete the square, we can write this as:
y = x^2 + 2*1*x - 2
Now we can add and subtract 1
y = x^2 + 2*1*x + 1 - 1 - 2
y = (x^2 + 2*1*x + 1) - 3
The thing inside the parentheses can be written as:
x^2 + 2*1*x + 1 = (x + 1)^2
Then the quadratic equation will be written as:
y = (x + 1)^2 - 3
This is the vertex form.
b) Now we want to know if the vertex is a minimum or a maximum.
Remember that the leading coefficient tells use if the graph of the function opens up or down.
If the leading coefficient is positive, the graph opens up (then the vertex is a minimum)
If the leading coefficient is negative, the graph opens down (then the vertex is a maximum)
In this case, we can write:
y = 1*(x + 1)^2 - 3
The leading coefficient is 1, positive.
Then the vertex is a minimum.
c) The coordinates of the vertex are:
Remember that in the vertex form:
y = (x - h)^2 + k
the vertex is (h, k)
Then the vertex of our equation is:
(-1, - 3)
Related Questions
which number is a composite
11, 5 , 9, or 2
(i need an answer asap
Answers
Answer:
2
Step-by-step explanation:
if you decrease £40 by 25% what do you get? i'm really bad at dividing and all that..
Answers
Answer:
£30
Step-by-step explanation:
hii :)
to solve this you can divide 40 by a hundred (to find 1%) and multiply that by 25 percent (to get 25% of 40) and then subtract that to find the decrease of 40 by 25%.
so 40/100=0.4
0.4*25=10
40-10= £30
hope this helped :)
Elizabeth buys 50 meters of ribbon to make bows for the cheer squad. Each bow uses 1.3 meters of ribbon. How many bows can Elizabeth make? *
Answers
Answer:
38 bows
Step-by-step explanation:
50 ÷ 1.3 ≡ 38 6/13
38 × 1.3 = 49.4
Since you cant make 6/13 of a ribbon, Elizabeth would be able to make 38 bows.
A room is 90 inches wide and 245 inches long. What is the area of the room?
Answers
Answer:
22050 inches
Step-by-step explanation:
To find the area, multiply length times width.
90*245=22050.
So, the room is 22050 square inches.
Answer:
22050
Step-by-step explanation:
can someone solve this for me using pemdas
Answers
Answer:
24
Step-by-step explanation:
(25-10) ÷ 5 × 8
15 ÷ 5 × 8
3 × 8
24
Answer:
24
Step-by-step explanation:
Any work inside parentheses must be done first: (5^2 - 10). Also:
Exponentiation is done before addition/subtraction: 5^2 - 10 = 25 - 10 = 15
So now we have 15 / 5 * 2^3 and recognize exponentiation again:
15 / 5 * 8
Then, since multiplication and division have the same order of priority,
carry out the division in 15/5 and then multiply the result (3) by 8
to obtain 24 (final answer)
heeeeeeeeeeeeeeeeelp
Answers
Answer:
well i know 3 is the lowest but i don't know how high it goes.
Range is where the graphs highest and lowest.
Step-by-step explanation:
https://youtu.be/fyROLkZc75E
Please help! This is due soon
Answers
Answer:
slope is 1/2
Step-by-step explanation:
u get brainliest if you anser first and is right if i get this wrong i fail pls help me
for 50 points
Answers
due tmr help plssssss‼️
Answers
Answer:
5π units
Step-by-step explanation:
The arc length of a semicircle is calculated as
length = [tex]\frac{1}{2}[/tex] πd ( d is the diameter ) , then
length = [tex]\frac{1}{2}[/tex] π × 10 = 5π units ← exact answer
How do I solve these problems?
Answers
Answer:
1.) The 1ˢᵗ three term is (-32), (-7) and 18
2.) The 1ˢᵗ three term is 127, 106 and 85
Step-by-step explanation:
1.)Here,
First Term = a₁ = - 32
Common Difference = (d) = 25
Now, For 1ˢᵗ three term,
n = 1
a₁ = - 32
n = 2
aₙ = a + (n - 1)d
a₂ = (-32) + (2 - 1) × 25
a₂ = (-32) + 1 × 25
a₂ = (-32) + 25
a₂ = -7
n = 3
aₙ = a + (n - 1)d
a₃ = (-32) + (3 - 1) × 25
a₃ = (-32) + 2 × 25
a₃ = (-32) + 50
a₃ = 18
Thus, The 1ˢᵗ three term is (-32), (-7) and 18
2.)Here,
First Term = a₁ = 127
Common Difference = (d) = -21
Now, For 1ˢᵗ three term,
n = 1
a₁ = 127
n = 2
aₙ = a + (n - 1)d
a₂ = 127 + (2 - 1) × (-21)
a₂ = 127 + 1 × (-21)
a₂ = 127 - 21
a₂ = 106
n = 3
aₙ = a + (n - 1)d
a₃ = 127 + (3 - 1) × (-21)
a₃ = 127 + 2 × (-21)
a₃ = 127 - 42
a₃ = 85
Thus, The 1ˢᵗ three term is 127, 106 and 85
-TheUnknownScientist
Ashley is training to run a
marathon. On Monday,
she runs 21 miles in 3
hours
COP=??
Answers
Answer:
7
Step-by-step explanation:
Answer:
what is a COP huhhh?????
The graph of the function f(x)=ax^2+bx+c is given. Could the factors f(x) be (x+2) and (x-3)? Based on the graph, explain why or why not.
Answers
find the slope of the line that passes through the points (4,-3) and (7,12)
Answers
Answer:
8/10
Step-by-step explanation:
12 - 4 8
-------- = -----
7 - (-3) 10
Answer:
5
Step-by-step explanation:
y2 - y1 / x2 - x1
12 - (-3) / 7 -4
15 / 3
5
Answer correctly for brainly
Answers
Answer:
graph D. it shows how much has you have at the beginning and ascends down to what you have left at 500
Answer:
Graph D
Step-by-step explanation:
With the other graphs, the information is too spread out or confusing. Graph D sums it up properly and makes it easy to read and understand.
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.
Answers
Answer:
[tex]6(x-10)(x+9)[/tex]
Step-by-step explanation:
First, make A equal one by factoring out the greatest common factor, 6. This makes the new expression [tex]6(x^{2} +x-90)[/tex]. Then, factor the remaining polynomial by finding two numbers that multiply to -90 and add to 1. These two numbers are -10 and 9. So, add each term to x and then multiply to get the final answer, [tex]6(x-10)(x+9)[/tex].
please help me i can't seem to get it
Answers
Answer C
Step-by-step explanation:
Explanation
Jack split 25 jellybeans between his brother and himself so that his brother has one more than twice the number Jack has. How many jellybeans does each have?
Answers
And his brother has 17
Answer:
Jack has 8 and his brother has 17
Step-by-step explanation:
j = # jack has
b = # brother has
j + b = 25
b = 1 + 2j (brother has one more than twice the amount jack has)
j + 1 + 2j = 25
3j = 24
j = 8
b = 25-8 or 17
Juan tiene un bidón de 5 litros de capacidad, llenado hasta los 2 1/3 litros. ¿Cuántos litros le faltan para llenarlo?
Answers
Answer:
nwhbjwhr
Step-by-step explanation:
ewrwrwrwewe
△ABC is reflected across the y-axis. The result is labeled △DEF. What must be true of angles A and D?
∡A is one−half of ∡D.
∡A is twice ∡D.
The angles are congruent.
Answers
Answer:
angles remain congruent
Step-by-step explanation:
all transformations, except dilations, do not change lengths of sides or angle measures
A quadratic function y=f(x) is plotted on a graph and the vertex of the resulting parabola is (−5,−3). What is the vertex of the function defined as g(x)=−f(x)+3?
Answers
Answer:
(-5 , 6)
Step-by-step explanation:
f(x) = (x - (-5))² - 3 ... vertex (h , k) : (-5 , -3) y = (x-h)² + k
g(x) = -f(x) + 3 = -((x+5)² - 3) + 3 = -(x + 5)² + 6
vertex of g(x) is : (-5 , 6)
5 1⁄3 - 4 5⁄6
help
NOQWWWWW
Answers
= 16/3 - 29/6
=32/6- 29/6
=32-29/6
= 3/6
= 1/2
Pls help me with this no links please and Thank you
Answers
Answer:
im sorry you need to take a better pic i can see the graphs
Portable telephones can
weigh as little as 8 ounces. How many
pounds is thiS
Answers
(Divide by 16 to get the answer)
Steve ran a 12-mile race at an average speed of 8miles per hour. If Adam ran the same race at an average speed of 6 miles per hour, how many minutes longer did Adam take to complete the race than did Steve?
Answers
Please help me NO LINKS PLEASEE
Answers
Answer:
(-1, -5)
Step-by-step explanation:
going to the left makes you go into the (-, +) plane and going down from there makes you go into the (-, -) plane.
The area of a parcel of land can be represented by the expression 9x2 - 6x + 10. The parcel must be divided into 3 equal parts. What is an expression that represents the area of each part?
A) 3x2 - 2x + 3 1 3
B) 9x2 - 6x + 13
C) 9x6 - 6x3 + 10
D) 27x2 - 18x + 30
Answers
Hope this helps!!
Complete the square to write each equation in vertex form. Then, state whether the vertex is a minimum or a maximum and give its coordinates.
Answers
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
• If a > 0 then vertex is minimum
• If a < 0 then vertex is maximum
Given
y = x² + 6x + 10
(a)
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 6x
y = x² + 2(3)x + 9 - 9 + 10
y = (x + 3)² + 1 ← in vertex form
(b)
Since a = 1 > 0 then vertex is a minimum
(c)
(h, k ) = (- 3, 1 ) ← coordinates of vertex
Help help help help help
Answers
Answer:
area = 254.5 m²
Step-by-step explanation:
area = πr² = (3.14159)(9²) = 254.46 m²
If you know how to do box and whisker plot pls answer this because I forgot how to do it
Answers
Answer:
A box and whisker plot is a way of summarizing a set of data measured on an interval scale. It is often used in explanatory data analysis. ... In a box and whisker plot: the ends of the box are the upper and lower quartiles, so the box spans the interquartile range. the median is marked by a vertical line inside the box.
Step One: The first step to creating a box and whisker plot is to arrange the values in the data set from least to greatest.
Step Two: Identify the upper and lower extremes (the highest and lowest values in the data set).
The lower extreme is the smallest value, Which in this case is 31
The upper extreme is the highest value which is62
Step Three: Identify the median, or middle, of the data set.
Which is 50 in this case
Step Four: Identify the upper and lower quartiles.
To find the lower quartile and the upper quartile, start by splitting the data set at the median into lower and upper regions.
The upper quartile is the median of the upper region and the lower quartile is the median of the lower region.
Step-by-step explanation:
Also, your answer is C.
Multiple Choice 8th Grade Math, please help your a legend if so!
Answers
Answer:
2
Step-by-step explanation:
Answer:
It's 2 weve done the worksheet ;)
Step-by-step explanation: