Answers
Answer:
The vertex form equation for the given graph is y = -(x - 2)² + 2
Step-by-step explanation:
The vertex form of the quadratic equation is y = a(x - h)² + k, where
a is the coefficient of x²(h, k) are the coordinates of the vertex pointFrom the given figure
∵ The graph is a parabola the graph of the quadratic equation
∵ Its maximum point is (2, 2)
∴ Its vertex is (2, 2)
→ By using the facts above
∴ h = 2 and k = 2
→ Substitute h, k in the form of the equation above
∴ y = a(x - 2)² + 2
→ To find a substitute x and y in the equation by a point on the curve
∵ The point (0, -2) lies on the parabola
∴ x = 0 and y = -2
→ Substitute them in the equation
∵ -2 = a(0 - 2)² + 2
∴ -2 = a(-2)² + 2
∴ -2 = a(4) + 2
∴ -2 = 4a + 2
→ Subtract 2 from both sides
∴ -4 = 4a
→ Divide both sides by 4
∴ -1 = a
→ Substitute it in the equation above
∴ y = -1(x - 2)² + 2
∴ y = -(x - 2)² + 2
∴ The vertex form equation for the given graph is y = -(x - 2)² + 2
Related Questions
Joe is installing a light fixture on a wall using a 10 foot ladder. A flower garden is planted along the wall, so Joe must place his ladder 6 feet away from the wall. How high up the wall will his ladder reach?
Answers
Answer:
The ladder is 8 feet high up on the wall.
Step-by-step explanation:
Let the height up of the ladder on the wall be represented by h. The ladder leaning on the wall, wall and distance of the foot of ladder from the wall form a right angled triangle.
So, applying the Pythagoras theorem;
[tex]/hyp/^{2}[/tex] = [tex]/adj 1/^{2}[/tex] + [tex]/adj 2/^{2}[/tex]
[tex]/10/^{2}[/tex] = [tex]/6/^{2}[/tex] + [tex]/h/^{2}[/tex]
100 = 36 + [tex]h^{2}[/tex]
so that,
[tex]h^{2}[/tex] = 100 - 36
= 64
⇒ h = [tex]\sqrt{64}[/tex]
= 8 feet
The ladder is 8 feet high up on the wall.
Which statement about converting metric units of measurement is true? Use the metric table to help answer the question.
Metric Table
kilo-
hecto-
deka-
unit
deci-
centi-
milli-
1,000
100
10
1
0.1
0.01
0.001
To find the number of hectometers in 87 centimeters, move the decimal point 4 units to the left.
To find the number of meters in 9,382 centimeters, move the decimal point 2 units to the right.
To find the number of kilometers in 6.39 decimeters, move the decimal point 3 units to the left.
To find the number of dekameters in 18 kilometers, move the decimal point 3 units to the right.
Answers
Answer:
To find the number of hectometers in 87 centimeters, move the decimal point 4 units to the left.
Mark me brainliest if I am right...PLEASE
Answer:To find the number of hectometers in 87 centimeters, move the decimal point 4 units to the left.
Step-by-step explanation:
a person is paying $10 per week to a friend to repay a $100 loan
Answers
Answer:
It would take the person 10 weeks to pay the friend back
Step-by-step explanation:
Don't know is this was the question :l
Answer:
y=-10x+100
Step-by-step explanation:
Cross multiply
23/3 / 21=
Answers
Answer:
161
Step-by-step explanation:
cancel 3 and 27 that gives u 7.
multiply 23 and 7 that gives u 161
I play the trombone and idk what these notes are I think the first one is a second position and the second note is a fourth position but I’m not sure :(
Answers
Answer:
i found this picture on google i just looked up. it should have your answer here. i play flute, so i dont understand it all that much :/
hope this helps
second pic is a flute chart ;P
Step-by-step explanation:
CSCB-CSCß-cos2B = 2-sinß
Answers
Answer:
more free points thanks bro
Step-by-step explanation:
ya yeet
Answer:
sin
Step-by-step explanation:
15 woman working 8 hours a day can harvest a cassava farm in 10 days. how long will it take 20 women working 5 hours a day to harvest the same farm
Answers
Answer: 37.5
Step-by-step explanation To get the wander to this question, you should divide 15 by 8 to get the decimal number. Then, after you want to multiply that decimal 20 times. I hope this helped! And it would mean so much to me if I could have brainliest.
how to convert 1 1/2
Answers
Answer:
3/2
Step-by-step explanation:
Step 1
Multiply the denominator by the whole number
2 × 1 = 2
Step 2
Add the answer from Step 1 to the numerator
2 + 1 = 3
Step 3
Write answer from Step 2 over the denominator
3/2
The scale drawing below shows the length of a soccer field as 6 inches. The actual length of a soccer field is 300 feet. If the width of the field is 180 feet, then what should the width of the scale drawing be in inches?
Answers
Answer:
width of the scale 10.8 inches
Step-by-step explanation:
write the fraction or mixed number as a decimal
[tex]1 \times \frac{7}{8} [/tex]
Answers
A map is drawn using a scale of 1 centimeter to 25 kilometers.
What actual distance is represented by a map length of 3.2 centimeters?
Enter the correct answer in the box.
Answers
Answer:
3.2 cm on map represents 80 kilometers of actual distance.
Step-by-step explanation:
It is given that the scale is:
1 cm = 25 km
And we have to find the distance that will be represented by 3.2 centimeters of length on the map.
Let x be the number of kilometers represented by 3.2 cm
[tex]\frac{1}{25} = \frac{3.2}{x}\\x = 3.2 * 25\\x = 80[/tex]
Hence,
3.2 cm on map represents 80 kilometers of actual distance.
Please HELP ASAP 31 points on
Answers
Answer:
It's way too small and I can't read it...
Step-by-step explanation:
PLEASE HELP!!!! WILL GIVE BRAINLIEST!!!!!
1. How do you dilate a figure on the coordinate plane and determine its scale factor?
2. How do you determine if polygons are similar?
3. Explain one way can you determine if two triangles are similar, without knowing all the angle
or side measurements.?
Answers
Answer:
1. You can look at side measurements. Angle measurements will not change so do not use them as reference. For example, if a rectangle has one side as 7 and the other 3, then the scale factor of a rectangle with a side of 21 and 9 would be 3, because 21÷7 is 3 or 9÷3 is 3.
2. You can determine a polygon is similar by having the same angles and/or similar sides.
3. All you need is one side and one angle if the angle and side are opposit each other, so a and A or b and B or c and C. If this is not represented in a problem then you can use 2 angles and 1 side or 1 angle and 2 sides to figure out if they are similar.
GUYS!!!!!!!!!!!!!!!!!! NEED HELP ASAP !!!!!!!!!!!!!!!!!
WHATS 1+1 ?!?!?!?! I CANT FIGURE IT OUT!!!!!!!!!!!!!
Answers
What is a function in math?
if you explain I will make you brainiest!
Answers
Answer:
A function is an equation in math that connects an input to a given output.
Step-by-step explanation:
-2/5x-9<9/10 Solve the inequality. Please help. YOU'LL BE THE BRAINLYEST!!!
Answers
Answer:
x>-99/4
Step-by-step explanation:
Darius takes his family on an afternoon boat ride.
Going through York Canal, he drives 5 miles in 15 minutes.
Later on as he crosses Stover Lake, he drives 30 minutes at the same average speed.
Which statement about the distances is true?
Answers
Help me if your good at math,,,
Answers
Answer:
a. -12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define
h(r) = (2/3)r - 6
h(-9) is r = -9
Step 2: Evaluate
Substitute: h(-9) = (2/3)(-9) - 6Multiply: h(-9) = -6 - 6Subtract: h(-9) = -12And we have our answer!
Answer:
a is correct
Step-by-step explanation:
what’s 8.43 x 10^7 in standard form?
Answers
Simply move the decimal place to the right 7 places
Please help im in the bathroom doing my Alger fa because I don’t want to go in person
Answers
Answer:
(8,-3)
Step-by-step explanation:
this is the point where the 2 lines intersect
Answer: 24
Step-by-step explanation: beacufg
how many times does 3 go into 8000
Answers
Answer:
a lot
Step-by-step explanation:
2666
What is the midpoint of the class interval 800-999?
Answers
Answer:
899.5
Step-by-step explanation:
Find the variance of: 2 4 5 6 7 9 10
Answers
Answer:
s = 7.811 ¯ 6
Step-by-step explanation:
x = 2 + 4 + 5 + 6 + 7 + 9 + 10 /7
¯ x = 43 /7
s = ( 2 − 6.1 ) 2 + ( 4 − 6.1 ) 2 + ( 5 − 6.1 ) 2 + ( 6 − 6.1 ) 2 + (7 − 6.1 ) 2 + ( 9 − 6.1 ) 2 + ( 10 − 6.1 ) 2/ 7 − 1
s = 7.811 ¯ 6What is the measure of \large \angle V?
Answers
Answer:
THe interior angles of any triangle equal 180
THerefore 48+87+v=180
48+87+v=180
87+v=132
v=45
Step-by-step explanation:
Sarah tosses a coin and spins a spinner
Answers
Answer:
Good for her ig
Step-by-step explanation:
8lb ham for $9.60 or 6lb ham for $7.50
Answers
Answer:
if ur asking which is a better deal, then it's the 8 lb ham for 9.60
Step-by-step explanation:
Answer:
8lb ham for $9.60
Step-by-step explanation:
Write an equation of a line perpendicular to y=-4x+9 that has a y-intercept of 7.
Use y=mx=b
Answers
Answer:
9
Step-by-step explanation:
easy
Which graph represents a linear function?
Answers
Answer:
That graph in the picture is not linear
Step-by-step explanation:
The graph does not go up or go down the same each unit
Answer:
not linear
Step-by-step explanation:
if it was linear there would be a diagonal straight line.
linear indicates there is a consistent ratio of x values and y values.
4. What are the different types of auto insurance
plans?
Answers
Answer:
auto liability coverage, uninsured and underinsured motorist coverage, comprehensive coverage, collision coverage, medical payments coverage and personal injury protection
Step-by-step explanation:
Solve the system of equation 0.4x – 3y = 7
3x + 14y = 10 using Cramer's Rule.
Answers
Answer:
for 0.4x – 3y = 7
Step-by-step explanation:
The answer is Changes made to your input should not affect the solution:
(1): "0.4" was replaced by "(4/10)".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(4/10)*x-3*y-(7)=0
STEP
1
:
2
Simplify —
5
Equation at the end of step
1
:
2
((— • x) - 3y) - 7 = 0
5
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 5 as the denominator :
3y 3y • 5
3y = —— = ——————
1 5
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2x - (3y • 5) 2x - 15y
————————————— = ————————
5 5
Equation at the end of step
2
:
(2x - 15y)
—————————— - 7 = 0
5
STEP
3
:
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 5 as the denominator :
7 7 • 5
7 = — = —————
1 5
Adding fractions that have a common denominator :
3.2 Adding up the two equivalent fractions
(2x-15y) - (7 • 5) 2x - 15y - 35
—————————————————— = —————————————
5 5
Equation at the end of step
3
:
2x - 15y - 35
————————————— = 0
5
STEP
4
:
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
2x-15y-35
————————— • 5 = 0 • 5
5
Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
2x-15y-35 = 0
Equation of a Straight Line
4.2 Solve 2x-15y-35 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x-15y-35 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 7/-3 so this line "cuts" the y axis at y=-2.33333
y-intercept = 35/-15 = 7/-3 = -2.33333
Calculate the X-Intercept :
When y = 0 the value of x is 35/2 Our line therefore "cuts" the x axis at x=17.50000
x-intercept = 35/2 = 17.50000
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.333 and for x=2.000, the value of y is -2.067. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.067 - (-2.333) = 0.267 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 0.267/2.000 = 0.133
Geometric figure: Straight Line
Slope = 0.267/2.000 = 0.133
x-intercept = 35/2 = 17.50000
y-intercept = 35/-15 = 7/-3 = -2.33333