HELP PLEASE!!!
Identify a point and two x intercepts to write the x-intercept form equation of each parabola.
Answers
x intercepts are 5 and 7
The third point I used was (6,-2); however, you can use any other point you want as long as it's not one of the x intercepts mentioned.
==========================================================
Explanation:
The x intercepts are 5 and 7, where the parabola crosses the x axis. Because of these roots, the two factors are x-5 and x-7.
We can think of the root x = 5 turning into x-5 = 0 after subtracting 5 from both sides. The same goes for x = 7 turning into x-7 = 0.
Put together, the two factors lead to (x-5)(x-7) and we get the equation y = (x-5)(x-7). Plugging either x = 5 or x = 7 into this equation produces y = 0.
-------------------
Notice that plugging in x = 6 leads to...
y = (x-5)(x-7)
y = (6-5)(6-7)
y = (1)(-1)
y = -1
However, the graph shows that x = 6 should lead to y = -2 instead. To fix this, we can stick a 2 out front like so
y = 2(x-5)(x-7)
y = 2(6-5)(6-7)
y = 2(1)(-1)
y = -2
The error has been fixed. As you can see, we need this third point to help nail down the parabolic equation. You can pick any other x value you want as long as it's not 5 or 7.
-------------------
Let's try another x value. Let's say we pick x = 8
y = 2(x-5)(x-7)
y = 2(8-5)(8-7)
y = 2(3)(1)
y = 6
We see that x = 8 leads to y = 6. This matches what the graph shows that (8,6) is a point on the parabola. I'll let you try other x values.
-------------------
In short, we used the roots 5 and 7 to generate the partial factorization (x-5)(x-7). Then we used a third point (6,-2) to help determine the coefficient out front which was 2.
So after using that point, we go from y = (x-5)(x-7) to y = 2(x-5)(x-7) which is the final answer. This is considered x-intercept form because we can quickly read off the x intercepts from this equation.
Related Questions
I need help
(No link please)
Answers
Answer:
the formula for finding the perimeter of a rectangle is P=2L+2W
an example of how to find the perimeter is
Explanation:
For a rectangle, its perimeter is the sum of all for sides.
The rectangle has a perimeter of 54. Find the lengths of the unknown side. That is, find S.
54=20+20+S+S
Simplify
54=40+2S
Solve for S
14=2S
S=7
Step-by-step explanation:
The base of the following pyramid is a square. If the volume of
the pyramid is 360 feet^3, what is the missing length? Round the
answer to the nearest hundredth.
Answers
Answer:
h = 12.52 ft
Step-by-step explanation:
volume of pyramid is 1/3*b*l. b is the base and l is the height we know that this equals 360 because it is given in the text. we also know b=8^2 since the base is a square so b=64. divide 360 by 1/3*64*pi to get l, l=5.3715. next we will use the pythagorean theorem to find h. first find the diagonal of the base: 8sqrt(2), now using the pythagorean theorem, we have h^2=5.3715^2 + (8sqrt(2))^2= 28.8528+128=156.8528. square root to get12.5241
Suppose that the functions f and g are defined for all real numbers x as follows.
f(x)=x+3
g(x) = 4x+4
Answers
Step-by-step explanation:
when you do an arithmetic operation to functions, you do it for the defining expressions.
so,
(f+g)(x) = (x + 3) + (4x + 4) = x + 3 + 4x + 4 = 5x + 7
(f*g)(x) = (x+3)*(4x+4) = 4x² + 12x + 4x + 12 = 4x² + 16x + 12
= 4(x² + 4x + 3)
(f-g)(4) = (4+3) - (4×4+4) = 7 - (16+4) = 7 - 20 = -13
Please help. Will give brainiest.
Write the equation of the line, in point-slope form. Identify (x 1 , y 1 ) as the point (-2, 2). Use the box provided to submit all of your calculations and final answers.
Answers
y-2=(-x+2)
point slope
equation is
y-y1=m(x-x1)
The box plots below show the average daily temperatures in January and December for a US city:
January
TH
December
What can you tell about the means for these two months (1 point)
Answers
Answer:
like i said no graph i cant help
Step-by-step explanation:
Graph the triangle with the given vertices. Find the length of the hypotenuse of the triangle. Assume a is a positive number.
X(0,0)
Y(a,2)
Z(a,0)
Answers
[tex]\\ \sf\longmapsto XY=\sqrt{x^2+y^2}[/tex]
[tex]\\ \sf\longmapsto XY=\sqrt{a^2+2^2}[/tex]
[tex]\\ \sf\longmapsto XY=\sqrt{a^2+4}[/tex]
[tex]\\ \sf\longmapsto XY=2+a[/tex]
Level: Easy
A football team loses 6 yards on their first play. It gains 8 yards on the next play. Which number line best represents the sum -6+8?
A)
B)
C)
D)
Answers
Please answer this question. No links :)
Answers
Step-by-step explanation:
[tex]\frac{rise}{run}[/tex]
Initially, as X increases, Y stays constant.
Then, between x = 3 and x = 5, the graph rises by 4 and runs by 2, or rises by 2 and runs by 1, so the slope is 2.
Between x = 5 and x = 9, the graph "rises" by -1 and runs by 1, so the slope is -1.
The greatest value of y is 4 at x = 5. (5, 4)
Answer:
Initially, as x increases, y remains constant.
Afterward, the slope of the graph of the function is equal to 2 for all x between x = 3 and x = 5.
The slope of the graph is equal to -1 between x = 5 and x = 9.
The greatest value of y = 4, and it occurs when x = 5.
Step-by-step explanation:
Slope = [tex]\frac{rise}{run}[/tex]
The rise is how much it increases by y (up or down), and the run is how much it increases by x (right or left).
From 3-5 the slope = [tex]\frac{4}{2}[/tex] = 2 → it goes up 2 units for every one unit right.
From 5-9 the slope = [tex]\frac{-4}{4}[/tex] = -1 → it goes down (-) 1 unit for every one unit right.
Find the equation of the line L.
Answers
Answer:
y = ([tex]-\frac{1}{2}[/tex])x + 4
Step-by-step explanation:
(x1,y1) = (0,4) ; (x2,y2) = (8,0)
The equation will look like y=mx+b
Slope m = [tex]\frac{rise}{run}[/tex] = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{0-4}{8-0}[/tex] = [tex]\frac{-4}{8}[/tex] = [tex]-\frac{1}{2}[/tex]
Next, substitute either x1y1 or x2y2 (it's gonna give the same answer anyways) and m to the equation y=mx+b to find b.
y=mx+b
0 = ([tex]-\frac{1}{2}[/tex])8 + b
0 = -4 +b
0+4 = -4 +4 +b
b=4
Then substitute b and m to the equation y=mx+b
y = mx + b
y = ([tex]-\frac{1}{2}[/tex])x + 4
6th Grade End-of-Module Review Part-xwhole Name Adam Robertson Date 1/12/21 1. Jazzlyn is applying for a job online. She has completed 12 questions. Throughout the application, a bar shows up to represent what percentage of questions she's completed. The progress bar currently shows 25%How many questions are there for the job application? Use a table, diagram, or equation to justify your answer.
Answers
Answer:
48 questions.
Step-by-step explanation:
x is for the unknown variable, the number you are trying to figure out.
12= 25%x
if you convert to a fraction, 12 is 1/4 of x. if you then multiply your answer by 4, 12 is 25% of 48.
to figure this out you can also ask, 12 is 25% of what number?
is this true or false |-2.9|> 2.6
Answers
Hello! :)
I will start by explaining what the l l notation means.
It means "absolute value" or a number's distance from zero.
Absolute value is always positive. Remember this:
lal=a
l-al=a
Now, using this, let's solve our math problem.
l-2.9l>2.6
2.9>2.6
Is this statement true? Is 2.9 greater than 2.6? Yes, it is. Therefore, the statement is true.
Hope it helps.
Feel free to ask me if you have any questions.
~A smiley teen who adores helping others
[tex]MagicalNature[/tex]
Answer:
True
Step-by-step explanation:
The absolute value of -2.9 is 2.9.
So 2.9>2.6
Remember, the absolute value of a number is always nonnegative (positive or zero). If a number is negative, negating that number will make it positive.
helpppppp plzzzzzz is fue today
Answers
Answer:
a) 3
Step-by-step explanation:
that's the correct answer
2-7/9x=5/6 without fractions
Answers
Answer:
x=0.6 repeating (meaning 6 is repeating so this is a repeating decimal)
Write the equation of the line in fully simplified slope-intercept form.
Answers
Answer:
y = 4/3x - 3
Step-by-step explanation:
1. Find two pints on the line: ((3,1) and (6, 5).
2. Find the slope: Slope = (change in y-values)/(change in the x-values).
Slope = (5 - 1)/(6 - 3) = 4/3
3. Use the slope and one point and substitute into y = mx + b to solve for "b"
y = mx + b slope = 4/3 and point (3, 1)
1 = 4/3(3) + b 4/3 · 3/1 = 12/3 = 4
1 = 4 + b
1 - 4 = b
-3 = b
4. Write the equation of the line: m = 4/3 and b = -3 Substitute into y = mx + b
y = 4/3x - 3
True or False?
If you graph the points (2,4) and (-1.-1). Do they would represent a proportional
relationship.
Answers
Answer:
1
Step-by-step explanation:
Mary is 4 years older than her sister Dawn.
In total the sisters have a combined age of 32.
Form an equation to show this. How old is Mary?
Answers
helpppppp plss thanks
Answers
Answer:
I can even see anything can you reupload your answer, please?
Step-by-step explanation:
A plane traveling to new york has 100 seats on board. if there are p passengers on the plane, which expression represents the number of empty seats there are on the plane
Answers
Hi math freindAnswer:
Step-by-step explanation:
Which ordered pair represents a solution to both equations?
Answers
Answer:
-3,-1
its obvious because all you're doing is plting points
Help me on this mathwork please
Answers
Answer:
m∠I = 56°
m∠1 = 30°
Step-by-step explanation:
Solve the System of Equations
3x^2-5y^2= 22
2x^2+4y^2 = 22
Answers
Lets try one way to solve this system. First, we want to isolate one of the unkown, lets choose y, so we need to remove x from an equation. In order to remove x from an equation, thats what we are going to do :
Line 1:
(3x² - 5y²) * 2 = 22 * 2
6x² - 10y² = 44
We simply multiplied Line 1 by the number 2, this doesn't change anything on the nature of Line 1.
Line 2:
(2x² + 4y²)*3 = 22*3
6x² + 12y² = 66
We simply multiplied Line 2 by the number 3, this doesn't change anything on the nature of Line 2.
Solving your system of equations is exactly the same thing as solving this new system of equation :
6x² - 10y² = 44
6x² + 12y² = 66
It is exactly the same. But it is easier now, because we can remove x from the equation simply by subtracting line 2 from line 1 :
L1 - L2 :
(6x² - 10y²) - (6x² + 12y²) = 44 - 66
6x² - 10y² - 6x² - 12y² = - 22
- 22y² = - 22
y² = 1
y = + 1 or y = - 1
We know have the value of y, we just have to replace it in the equation to solve the entire system :)
3x² - 5y² = 22
since y² will always be equal to one, wether y = 1 or y = - 1, we can write :
3x² - 5 = 22
3x² = 22 + 5
3x² = 27
x² = 27/3
x² = 9
x = + 3 or x = - 3
So the solutions are the following couples in the form (x,y) :
S = { (3 ; 1) , (-3;1) , (3 ; - 1) , (-3 ; -1))
Good Luck
Question 1 of 25
Which of these numbers is in the solution set of x- 12 = 3?
O A. 15
O B. -9
O C. 9
OD. 4
Answers
x-12=3 x=15
I WILL GIVE BRAINLIEST TO WHOMEVER ANSWERS (TRUTHFULLY) !!NO LINKS!!
Answers
Step-by-step explanation:
SAS ================
What it says:
If two sides and the angle between them on one triangle are congruent to the corresponding two sides and the angle between them on the other, the triangles are congruent.
Required information:
Two sets of congruent sides with a congruent angle between them
ASA ================
What it says:
If one side and both connected angles on one triangle are congruent to one side and both connected angles on the other, the triangles are congruent.
Required information:
One set of congruent sides with two sets of congruent angles on the sides
AAS ==================
What it says:
If two angles and the non-included side on one triangle are congruent to two angles and the non-included side on the other, the triangles are congruent.
Required information:
Two sets of congruent angles and one set of congruent non-included sides
HL =================
What it says:
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg on the other, the triangles are congruent.
Required information:
Congruent hypotenuse and congruent leg
A pyramid has a square base of length of 12m. Given the slant height of the pyramid is 15 m, draw its net and hence, find its total surface area.
Answers
Answer:
the surface area is 180 if u use multiplication
Step-by-step explanation:
the surface is 0.8 if you use devide
the surface is 3 if u use subtract
and the surface is 27 if you use addition
correct me if I'm wrong :)
A
Plz help!!!!!! !!!!!!!!!!!
Answers
Answer:
R is at the ordered pair (4, -2)
Step-by-step explanation:
triangles one and two are both isosceles meaning they each have two equal sides they each have a 30-degree angle explain why these triangles do not have to be similar to each other
Answers
Answer:
See below for answers
Step-by-step explanation:
These triangle do not have to be similar to each other because the 30° angles may not be located in the same place.
For example, place one 30° at the vertex of the triangle which is located where the two equal legs of the isosceles triangle are joined. The triangle angles measure are 30°, 75°, and 75°.
But if the 30° angle is one angle at the base of the isosceles triangle, then the angles measure are 30°, 30°, 120°.
30°
Δ Δ
30°
13. On a snow day, the temperature at 8 AM was 2°F. Later in the day the temperature rose 6º. What was the resulting temperature?
Answers
The resulting temperature was 8°F.
The first three terms in a pattern are shown in the
image below. How many circles would be in the
5th term?
A. 10
B. 15
C. 18
D.20
Answers
Answer: 15
Step-by-step explanation: you basically add n per sequence.
0+1 = 1
1+2 = 3
3+3 = 6
6+4 = 10
10+5 = 15
Hope this helps
The Western inventory was written by 4 different authors. Author A wrote 1/4 of the books, author b wrote 5/16 of the books, and author c write 3/8 of the books. What part of the inventory did author D write?
Answers
Answer:
Author D write 1/16 of the total number of books.
Step-by-step explanation:
Let the total number of books be b. Then the amounts written by the four authors would be represented by:
(1/4)A
(5/16)A
(3/8)A
( ? )A
Add these together, realizing that the LCD here is 16:
(4/16)A
(5/16)A
(6/16)A
( ? ) A
------------
(15/16)A must then equal the remainder of the work: (16/16)A
Thus, Author D wrote (1/16)A of the books. (Note that 4/16 + 5/16 + 6/16 + 1/16 = 1)
Author D write 1/16 of the total number of books.
An item priced at $500 is bought on hire purchase, where $200 deposit is required, along with 12 monthly instalments of $40. How much would be saved if bought with cash?