Answers
Answer:
Vertex form: y = -2(x - 1)²
Standard form: y = -2x² + 4x - 2
Step-by-step explanation:
Given the x-intercept as the vertex, (1, 0), and the y-intercept, (0, -2) as the two points on the graph of a parabola:
We can determine the equation by substituting these given values into the vertex form of the quadratic equation:
y = a(x - h)² + k
where:
a = determines the direction of where the graph opens, and the wideness or narrowness of the parabola.
(h, k) = vertex
Solve for the value of a:Use vertex: (1, 0) and y-intercept, (0, -2):
y = a(x - h)² + k
-2 = a(0 - 1)² + 0
-2 = a(-1)²
-2 = a(1)
-2 = a
Quadratic Equation:Vertex form:The quadratic equation in vertex form that matches the graph is:
y = -2(x - 1)² + 0 or y = -2(x - 1)² ⇒ This is the quadratic equation in vertex form.
Standard form:To transform the vertex form into the standard form, y = ax² + bx + c:
Simply expand the perfect square, (x - 1)², through FOIL method before distributing -2:
y = -2(x - 1)²
y = -2(x - 1)(x - 1)
y = -2(x² -2x + 1)
y = -2x² + 4x - 2 ⇒ This is the quadratic equation in standard form.
Related Questions
A hot air balloon is at an elevation of 425 feet. It descends 110 feet what is the elevation of the balloon?
Answers
Answer:
315
425 + -115 = 315 feet
Step-by-step explanation:
Answer:
The balloon will be at an elevation of 315 feet.
Step-by-step explanation:
425-110=315
Write the Equation
Equation
X Y
-2 5
-1 3
0 1
1 -1
y=-X+2
y=x+2
y=2x+1
y-2x+1
Answers
Answer:
y=-5×+13
Step1 inter change ×gy
4. Here are the steps Tyler took to solve the equation Vx+3 = -5.
Vx+3=-5
+ 3
x + 3 = 25
x= 22
a. Check Tyler's answer: Is the equation true if x = 22? Explain or show your
reasoning.
b. What mistake did Tyler make?
Answers
Answer:
vx=-5-3
Step-by-step explanation:
vx=,-8 oooooooookkk
you and your friends are going to the movies.You bought 5 tickets and spent 12.50 for popcorn.Your total was $80.Write and solve an equation to calculate the cost of each ticket
Answers
80=5x+12.5
We just use the equation y=mx+b. Where 80 is our Y, 5 is our slope, or m, and 12.5 is our constant, or b.
For the giggles I'll also solve the equation.
80-12.5=5x
67.5=5x
67.5 / 5 = x
13.5 = x
This means that each ticket was $13.5. Wow, that's an expensive ticket.
I hope this helps! :)
Answer:
I will answer soon aim coming
i need this one fast too so if you can please help fast
Answers
2x-y=4
-2x+y=7
is there a solution
Answers
[tex] \text{Given : 2x - y = 4 and x + 2y = 7}[/tex]
[tex] \text{Solution : according to the question here we are provided with} \\ \text{two equations separately. So, let's name them as eq(1) and eq(2).} \\ \text{ The rest is followed as we continue to get to our goal} \\ \\ \sf {1}^{st} \: equation : \\ \quad\dashrightarrow \frak{2x - y = 4} \\ \\ \quad \dashrightarrow \frak{ \red{x = \frac{y + 4}{2} }} \qquad \sf ...eq(1) \\ \rm{ now \: \: as \:per \: our \: plan \: we \: need \: to \: get \: eq(2) } \\ \\ \sf{ {2}^{nd} \:equation} : \\ \quad\dashrightarrow \frak{ x + 2y = 7} \\ \\ \quad\dashrightarrow \frak{ \red{y = \frac{7 - x}{2}}} \qquad \sf ...eq(2) \\ \\ \text{Now, finding x and y} \\ \\ \underline{ \frak{Finding \: x}}\\ \\ \quad \hookrightarrow \frak{x = \frac{y + 4}{2}} \\ \\ \quad \hookrightarrow \frak{2x = \frac{7 - x}{2} + 4} \\ \\ \quad \hookrightarrow \frak{2x = \frac{7 - x + 8}{2}} \\ \\ \quad \hookrightarrow \frak{2x = \frac{1 - x}{2}} \\ \\\quad \hookrightarrow \frak{4x = 1 - x} \\ \\ \quad \hookrightarrow \frak{5x = 1} \\ \\\quad \star \qquad \underline{ \boxed{ \green{ \frak{x = \frac{1}{5}}}}} \\ \\ \underline{ \frak{Finding \: y}} \\ \\ \quad \hookrightarrow \frak{y = \frac{7 - x}{2}} \\ \\ \hookrightarrow \frak{2y = 7 - \frac{1}{5} } \\ \\ \hookrightarrow \frak{2y = \frac{35 - 1}{5} } \\ \\ \hookrightarrow \frak{2y = \frac{34}{5}} \\ \\ \hookrightarrow \frak{y = \frac{34}{5} \times \frac{1}{2}} \\ \\ \hookrightarrow \frak{y = \frac{17}{5} } \\ \\ \star \qquad \underline{ \boxed{ \frak{ \green{y = 3 \frac{2}{5} }}}}[/tex]
Determine the inverse of the function
Answers
Replace every x with a y and replace every y with an x .
Solve the equation from Step 2 for y . ...
Replace y with f−1(x) f − 1 ( x ) . ...
Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.
Between what two whole numbers is 5/6 located on the number line? help please!
Answers
Answer:
Hello there!
5/6 is located between 0 and 1.
Step-by-step explanation:
5/6 is less than 1, because 1 = 6/6 in this scenario.
At the same time, it's greater than 0!
5/6 is located between 0 and 1 on the number line!
kate has $2.95 in quarters and nickels and the total number of ocins is 23 how many quarters and how many nickels does kat have
Answers
Answer: 9 quarters and 14 nickels
Step-by-step explanation:
9*25=225
14*5=70
225+70=295
The total number of nickels is 14 and the total number of quarters is 9 and this can be determined by forming the linear equation.
Given :
kate has $2.95 in quarters and nickels and the total number of coins is 23.
The following steps can be used in order to determine the total number of quarters and nickels Kat have:
Step 1 - Let the total number of quarters be 'x' and the total number of nickels be 'y'.
Step 2 - Remember one quarter is equal to $0.25 and one nickel is $0.05.
Step 3 - The total amount of money Kat has:
0.25x + 0.05y = 2.95 --- (1)
Step 4 - Total number of coins is given by:
x + y = 23
x = 23 - y --- (2)
Step 5 - Substitute the value of 'x' in equation (1).
0.25(23 - y) + 0.05y = 2.95
5.75 - 0.25y + 0.05y = 2.95
2.8 = 0.20y
y = 14
Step 6 - Now, substitute the value of 'y' in equation (2).
x = 23 - 14
x = 9
So, the total number of nickels is 14 and the total number of quarters is 9.
For more information, refer to the link given below:
https://brainly.com/question/11897796
Find the value of X in the following 3x+4=25
Answers
The answer is 7
Step-by-step explanation:
subtract 4 from 25 which is 21 than divide by 3 getting x =7
Answer:
x=7
Step-by-step explanation:
3x+4=25
3x=25–4
3x=21
X=21÷3
X=7
is 6,8,9 a pythagorem theorem? pls help me due rn
Answers
Answer:
No, it isn't.
Step-by-step explanation:
Pythagorean theorem is x^2 + y^2 = z^2.
6^2 + 8^2 = 9^2
36 + 64 = 81
100 = 81
So, it isn't.
Answer:
No.
Step-by-step explanation:
36+64 does not equal 9² (81)
help please how u do dis
Answers
Answer:
WR = 16
Step-by-step explanation:
The centroid M is the point where the 3 medians intersect
The median is a segment that goes from one of the triangle's vertices to the midpoint of the opposite side.
WY is a median of the triangle , then
WY = YR = 8
WR = wy + yr = 8 + 8 = 16
Using a riding lawn mower, Shane, the landscaper of a large park, can mow the lawn in 8 hours. With a small mower, her assistant Matt needs 14 hours to mow the same lawn. If Shane and Matt work together mowing the lawn, how long will it take them to mow the lawn?
Answers
Answer:
1 hour and 45 minutes
Step-by-step explanation:
I know this because you just need to divide the amount of hours that shane did it and the amount of time matt did it and then it will give you your answer
slope = -5/2,y-int=2
Answers
Answer:
Step-by-step explanation:
The equation of this line is:
y = -5/2 x + 2.
A deli owner sold 90 sandwiches in one day. Of those sandwiches, 36 were pastrami.
Write and solve an equation to show what percent of sandwiches sold were pastrami.
Drag tiles to complete the equation. Tiles may be used once or not at all.
p • __ = 36
plss help
Answers
Answer:
p · 90 = 36
p = 40%, 0.4, 4/10
Step-by-step explanation:
p · 90 = 36
p = 36/90
p = 4/10
p = 40%, or 0.4
-Chetan k
Benny has a baseball card collection he has 13,789 cards he wants to put the card in a scrapbook that holds 15 cars on a page how many pages does Denny need in his scrapBook.
Answers
Answer:
920 pages
Step-by-step explanation:
Divide 13,789 by 15, you should get 919.27 so just round up so you can hold all the cards.
HELP PLEASE !!!
Which angles are congruent
if RI ≅ IT, what angles are congruent? 1, 2, or 3?
*THERE SHOULD BE 2 ANSWERS*
Answers
the answer is 32 because it as shown it has 23 and 67
the angle 1 and 3 are congruey
Which figure best demonstrates the setup for the box method of finding the area of a triangle? On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and share 2 sides with the triangle. On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and the 3 points of the triangle touch the sides of the box. The box is 2 units larger than one side of the triangle. On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and all 3 points of the triangle are on the sides of the box. On a coordinate plane, a triangle is shown. A rectangular box is drawn around the triangle and 2 points of the triangle are on the box.
Answers
Answer:
C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The answer is C in Edge. Just took the assigment. Hope this helps! :)
Consider the line y=6/7 x -7. Find the equation of the line that is perpendicular to this line and passes through the point (6,-6). Find the equation of the line that is parallel to this line and passes through the point (6,-6) .
Answers
Answer:
[tex]y= -\frac76x +1[/tex]; [tex]y= \frac67x -\frac{78}7[/tex]
Step-by-step explanation:
We know from theory that two perpendicular lines have the product of their slope equal to -1. Let's find the second slope:
[tex]\frac67m = -1 \rightarrow m=-\frac76[/tex]
At this point we can just use the slope-point equation to get our first line:
[tex]y-y_0 = m(x-x_0)\\y-(-6) = -\frac76(x-6) \\y+6= -\frac76x +7\\y= -\frac76x +1[/tex]
Now, we know that two parallel lines have the same slope. Time to apply the same point-slope formula, with the original m this time.
[tex]y-(-6) = \frac67(x-6)\\y+6 = \frac67x -\frac{36}7\\y= \frac67x -\frac{36}7 -{\frac{42}7[/tex]
[tex]y= \frac67x -\frac{78}7[/tex]
The denominator of a fraction is four more than the numerator. If both numerator and denominator are decreased by one, the simplified result is 57. Find the original fraction. (Do NOT simplify.)
Answers
please help giving brainliest and big points it would be greatly appreciated :))
Answers
Answer:
X = 4 , Y = b , Z = 2a
Step-by-step explanation:
2b(2ab)² - a(2b²)² ← expand parenthesis
= 2b(4a²b²) - a(4[tex]b^{4}[/tex]) ← distribute parenthesis
= 8a²b³ - 4a[tex]b^{4}[/tex] ← factor out 4ab³ from each term
= 4ab³(2a - b)
Compare terms to XaY³(Z - b)
with X = 4 , Y = b , Z = 2a
En una panadería, con 80 kg de harina hacen 120 kg de pan. ¿Cuántos kilos de harina serían necesarios para hacer 360 Kg de pan?
Answers
Answer:
240 kg
multiplica 360 con 80 y luego dividelo por 120. Que equivale a 240, o divide 120 por 80 que te da 1.5 y multiplicalo por 240 que equivale a el total 360 Kg
Nothing, never wanted to post a question on here
Answers
What is the y-intercept of the graph shown below?
.....
Answers
Answer:
The y-intercept is -2.5.
Step-by-step explanation:
If you look at the graph, you can see that the blue line is landing on the -2.5 in the y-axis column. Therefore, -2.5 is your answer.
Does anyone know this?
Answers
Answer:
△RED~△TAN
Step-by-step explanation:
Both triangles are similar, even if they have different sizes. They still retain the same degrees.
Proof: Angle RED
180 - 110 - 28 to find m∠E.
m∠E = 42
m∠A = 42
m∠E = m∠A
I need help. I'm suppose to find the angle of "o"
Answers
Hope this helps, if you need an explanation just ask
whats the answer for this??
Answers
Step-by-step explanation:
what do you mean "what's the answer for this ?"
you only need to put 3 in place of x (that's what is meant by "x is 3" or x = 3) and then simply calculate.
you know what "squaring" ("something to the power of 2" or x²) means ? it means that you have to multiply that "something" by itself.
y = 3² + 11 = 3×3 + 11 = 9 + 11 = 20
that's all there is to this.
help me
[tex] \: [/tex]
A C E isoscles ACAR is inscribed in o E If mCR = 1300 Find:
11.m CAR
12. mACR
13. mARC
14. mAC
15. mAR
[tex] \: [/tex]
marking brainlist
with explanation
I will report nonsense answer
need properly answer
[tex] \: [/tex]
Answers
Answer:
#11m∠CAR = (1/2)mCR = (1/2)(130°) = 65°#12 and #13m∠ACR = m∠ARC = 1/2(180° - 65°) = (1/2)(115°) = 57.5° #14 and #15mAC = mAR = 2(m∠ACR) = 2(57.5°) = 115°Please help with this math problem!! :)
Answers
Answer:
Step-by-step explanation:
a^2 + B^2 = C^2
and all angle added together should make 180
the left box should be 20 and the right box should 17.321
2. If triangle ABC is congruent to triangle DEF by SAS, AB=DE,
Answers
Answer:
I can't Respond since I have no picture to help you or me
Step-by-step explanation:
Without the Picture I can't determine if the triangle ABC is congruent to triangle DEF by SAS, AB=DE