Answer:
The Graph of a Quadratic Function
A quadratic function is a polynomial function of degree 2 which can be written in the general form.
Step-by-step explanation:
Example: Graph: f(x)=−x2−2x+3.
Solution:
Step 1: Determine the y-intercept. To do this, set x=0 and find f(0).
f(x)f(0)===−x2−2x+3−(0)2−2(0)+33
The y-intercept is (0,3).
Step 2: Determine the x-intercepts if any. To do this, set f(x)=0 and solve for x.
f(x)000x+3x======−x2−2x+3−x2−2x+3x2+2x−3(x+3)(x−1)0−3orx−1x==Set f(x)=0.Multiply both sides by −1.Factor.Set each factor equal to zero.01
Here where f(x)=0, we obtain two solutions. Hence, there are two x-intercepts, (−3,0) and (1,0).
Step 3: Determine the vertex. One way to do this is to first use x=−b2a to find the x-value of the vertex and then substitute this value in the function to find the corresponding y-value. In this example, a=−1 and b=−2.
x====−b2a−(−2)2(−1)2−2−1
Substitute −1 into the original function to find the corresponding y-value.
f(x)f(−1)====−x2−2x+3−(−1)2−2(−1)+3−1+2+34
The vertex is (−1,4).
Step 4: Determine extra points so that we have at least five points to plot. Ensure a good sampling on either side of the line of symmetry. In this example, one other point will suffice. Choose x=−2 and find the corresponding y-value.
x −2 y 3f(−2)=−(−2)2−2(−2)+3=−4+4+3=3Point(−2,3)
Our fifth point is (−2,3).
Step 5: Plot the points and sketch the graph. To recap, the points that we have found are
y−intercept:x−intercepts:Vertex:Extra point:(0,3)(−3,0) and (1,0)(−1,4)(−2,3)
Answer:
solve graphically please send me by solving and clicking photo plzzzz
Answer:
Subtract 5x from both sides of the equation.
7y=1−5x
x+4y=−5
Divide each term by 7 and simplify.
y=17−5x/7
x+4y=−5
Subtract x from both sides of the equation.
y=1/7−5x/7
4y=−5−x
y=1/7−5x/7
Divide each term by 4 and simplify.
y=1/7−5x/7
y=−5/4−x/4
y=1/7−5x/7
Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution. (3,−2)
Step-by-step explanation:
Lian was asked to write an equation and solve this problem.
Shonda has some small spoons and 40 large spoons. If she has 68 spoons total, how many small spoons does Shonda have?
Lian’s work is shown below.
Steps
Lian’s Work
Step 1
s + 40 = 68
Step 2
s + 40 minus 40 = 68 minus 40
Step 3
s = 28
In which step, if any, did Lian first make a mistake in her work?
step 1
step 2
step 3
no mistake Who wanna mha (my hero academia anime rp wit me plz dont report)
Answer:
Its no mistake
Step-by-step explanation:
I got it right
find the discriminant of 2x square + x - 6 is equal to zero?
Answer:
When the discriminant value is zero, we get one real solution; When the discriminant value is negative, we get a pair of complex solutions; Standard Form. The standard discriminant form for the quadratic equation ax 2 + bx + c = 0 is. Discriminant, D = b 2 – 4ac. Where. a is the coefficient of x 2. b is the coefficient of x. c is a constant term.
Estimated Reading Time: 50 secs
Step-by-step explanation:
What is the equation of a line parallel to the line y = 4x - 5 with a y intercept of
3?*
HELPP PLEASE! ASAP!!
A farmer sells 6.1 kilograms of pears and apples at the farmer's market. 4 5 of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?
Answer:
1.6
Step-by-step explanation:
6.1 kilograms - 4.5 kilograms = 1.6 kilograms
There are 2 pigs, 1 cat, 3 goats, and 4 cows at the state fair. As people enter the barn area they are randomly given one animal to pet. What is the probability that a person will pet a goat? Write your answer as a fraction, decimal, and percent.
PLS ANSWER QUICK and pls dont answer with a website answer with the answer
Fraction:
Decimal:
Percent:
Answer:
3/10
Step-by-step explanation:
Probability will be the number of goats, since goats is what you're looking for, over the number of total animals. So that gives 3/10.
To get that as a decimal, divide 3 by 10. Then take your decimal and multiply it by 100 to give the percent.
c) Work out
√6 x √6 x √6
Answer:
√6 × √6 × √6 = 6√6
Step-by-step explanation:
[tex] \rm \sqrt{6} \times \sqrt{6} \times \sqrt{6} [/tex]
[tex] \rm = \sqrt{36} \times \sqrt{6} [/tex]
[tex] \blue{\boxed{\rm = 6 \sqrt{6} }}[/tex]
Identify the solution to the system
Answer:
The solution is where the two lines intersect so
(1, 3)
x= 1
y= 3
Step-by-step explanation:
HELPPPPP please :( thanks
Find the volume of the pyramid, given its slant height. Round them to the nearest tenth please.
Can you help me? I tried but I did not understand and thank you
9514 1404 393
Answer:
4. 1.3 cm³
5. 621.2 mm³
6. 116.5 m³
Step-by-step explanation:
The height to the peak of the pyramid is one side of the right triangle that has its hypotenuse equal to the slant height, and one leg equal to half the base side length. The Pythagorean theorem is used to find the height from the slant height (s) and the base length (b):
h = √(s² -(b/2)²)
The volume is found from the formula ...
V = (1/3)b²h
where b is the base length and h is the height found using the previous formula.
The tedious arithmetic is nicely done using a spreadsheet. Results are attached.
HELPPP ME PLEASE WOTH THIS PROBLEM
Answer:
Area = 220.8 units²
Step-by-step explanation:
Since, given regular hexagon is made up of 6 congruent triangles joined together.
Area of the given regular hexagon = 6(Area of ΔAOB)
Area of ΔAOB = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(AB)(OC)[/tex]
= [tex]\frac{1}{2}(9.2)(8)[/tex]
= 36.8 unit²
Therefore, area of regular hexagon = 6(36.8)
= 220.8 units²
pls help for #9! whats the area of the shaded region ?
Answer:
21.5
Step-by-step explanation:
square is 10x10 = 100
circle is A=πr2=π·5²≈78.54
100-78.54 = 21.46 = 21.5
Answer:
21.5 sq cm
Step-by-step explanation:
Area of Square:
A= LXW= 10x10= 100 sq cm
Area of Circle=
A=πr²
Radius= D/2= 10/2= 5 cm
A=3.14(5²)
A=3.14(25)= 78.5 sq cm
Shaded Region= 100-78.5= 21.5
The area of the shaded region is 21.5 sq cm.
Maria, Carolina and Pedro receives $1600 from their grandfather in ratio 7:5:4. calculate share of each.
Step-by-step explanation:
here's your solution
=> total money received by them = $1600
=> the given ratio are 7:5:4
=> let the ratio be X ,now
=> Maria = 7X
=> Carolina = 5X
=> Pedro = 4X
=> we know whole money = $1600
=> so, adding all
=>. 7x + 5x + 4x = $1600
=> 16x = $1600
=> x= $1600/16
=>. x = $100
now Maria = 7*100 = $700
Carolina = 5*100 = $500
Pedro = 4*100 = $400
hope it helps
Why was the United States interested in rebuilding the Japanese economy after World War II?
A
The United States feared the influence of communist countries in Japan.
B
The United States and Japan had a shared history of colonial oppression.
C
The United States wanted to make the Japanese pay war reparations.
D
The United States planned to occupy Japan for many years to come.
A $3,000 deposit for 66 months compounded at an annual interest rate of 1.6%. What is the interest and the account balance at the end of the 66 months
Answer:
interest: $275.77balance: $3,275.77Step-by-step explanation:
The account value is given by the compound interest formula:
A = P(1 +r/12)^n
Principal P invested at annual rate r compounded monthly for n months.
__
Using your parameters, the account balance would be ...
A = $3000(1 +0.016/12)^66 = $3275.77 . . . account balance
The interest is the difference between this balance and the original investment amount:
interest = $3000 -3275.77 = $275.77 . . . interest
Calcula el volumen, en centímetros cúbicos, de una habitación que tiene 5 m de largo, 4 m de ancho y 2.5 m de alto. V=50m ^3
Answer:
the volume is 50m^3
Step-by-step explanation:
The computation of the volume of the room is shown below:
As we know that
The Volume of the room = length × width × height
volume = 5m × 4m × 2.5m
= 50m^3
Hence, the volume is 50m^3
write a rule for the n th term of the geometric sequence for which a_1=11 and a_4=88
Answer:
Step-by-step explanation:
write a rule for the n th term of the geometric sequence for which a_1=11 and a_4=88
Which of the following length can represent a right triangle?
5,12,15
4,5,6
8,10,12
20,21,29
Answer:
20, 21, 29
Step-by-step explanation:
h²= p²+b²
29² = 20²+ 21²
What’s the value of x
What is the exact volume of the cylinder?
Enter your answer, in terms of it, in the box.
Answer:
volume of cylinder : πr²×h = π × 5² × 15 = 375π ≈ 1177.5 cm³
HELP ME PLEASE I NEED IT NOW
What two things make a graph proportional?
how to find surface area of trapezoid.
Answer: To find the area of a trapezoid, start by adding together the length of the bases, which are the 2 sides of the trapezoid that are parallel with each other. Then, multiply that number by the height of the trapezoid. Finish by dividing the product by 2 to find the area. Or check this image it can help u
Step-by-step explanation:
please help, I did it 3 times but can't seem to get is right
Answer:
A' = (-2,0)
Step-by-step explanation:
imagine a mirror being along the line y=2.
Then A's mirror image would appear at -2,0.
A recipe for one full cake calls for one fourth cup of sugarIf three eighths of a cup of sugar is used, how many cakes were made?
Answer:
1 1/2 cakes
Step-by-step explanation:
3/8 ÷ 1/4
3/8 * 4/1
12/8
3/2
1 1/2
Alice takes 4 white, 2 red, and 3 blue shirts on a trip. On the first day Alice will pick a shirt at random. What is the probability that she picks a red shirt?
Answer:2/9
Step-by-step explanation:
5 1/3 divided by 2/3
Draw a diagram
[tex]5\frac{1}{3} =\frac{16}{3}[/tex]
[tex]\frac{16}{3} -\frac{2}{3} \\=\frac{14}{3}[/tex]
Hope this helped!!!!!!!
[Help asap, will mark brainliest] Find the distance between the following pairs of points on the coordinate plane. Round to the nearest tenth if necessary.
The distance between point A and point D = units
Answer:
8.06 units = AD
(just write sq rt 65 = 8.062 ) then write or try sq rt of 65 to 3 sf = nearest tenth 8.06 tenth units rounded.
Step-by-step explanation:
AE = 7
ED = 4
We use Pythagoras Theorem as it is a right angle as AE^2 + ED^2 = AD^2
7^2 + 4^2 = AD^2
49 + 16 = 65 sq rt
sq rt 65 = AD^2 = 8.062^2
AD = 8.062 units
Solve y-7=3
Thank you
− 7 = 3
− 7 + 7 = 3 + 7
= 10