The point (4,-2) is the vertex of the graph of a quadratic function. The points (8,6) and (2,0) also fall on the graph of the function.
Part A:Complete the graph of this quadratic function by first finding two additional points on the graph.
Part B:What is the y-intercept of the graph?
Part C:What are the x-intercept?
Part D:Find the interval on which the rate of change is always positive.
Part E:What is the sign of the leading coefficient for this quadratic function? How do you know?
Answer:
Step-by-step explanation:
y = ax² + bx + c
~~~~~~~
(4, - 2), (8, 6), (2, 0)
a(4²) + b(4) + c = - 2
a(8²) + b(8) + c = 6
a(2²) + b(2) + c = 0
16a + 4b + c = - 2 .............. (1)
64a + 8b + c = 6 ............... (2)
4a + 2b + c = 0 ................. (3)
a = 0.5 ; b = - 4 ; c = 6
y = 0.5x² - 4x + 6
Part A: (0, 6), (6, 0)
Part B: (0,6)
Part C: (6, 0)
Part D: [ 4, ∞ )
The quadratic function has the form f(x) = ax² + bx + c, where a, b, and c are non-zero values, and the calculation of the values can be defined as follows:
Quadratic function:vertex point of graph function= (4,-2)
points= (8,6) and (2,0)
Using the formula of a quadratic function:
[tex]y = ax^2 + bx + c[/tex]
putting the value into the above-given formula:
[tex]\to (4, - 2), (8, 6), (2, 0)\\\\\to a(4^2) + b(4) + c = - 2\\\\\to 16 a + 4b + c = - 2.........................(a)\\\\\to a(8^2) + b(8) + c = 6\\\\\to 64a + 8b + c = 6......................................(b)\\\\\to a(2^2) + b(2) + c = 0\\\\\to 4a + 2b + c = 0................................(c)\\\\[/tex]
Computing the value of a,b, and c:
[tex]\to a = 0.5\\\\ \to b = - 4 \\\\ \to c = 6\\\\[/tex]
Putting the value of a, b, and c values into the quadratic function:
[tex]\to y = 0.5x^2 - 4x + 6[/tex]
So, the calculated points are:
Part A: (0,6)
Part B: (2,0) and (6,0)
Part C: x>4
Part D: positive the parabola upwards
Please find the correct question and graph file in the attachment.Find out more about the quadratic function here:
brainly.com/question/5975436
On Monday Sylvia spent 5/12 of a day driving to her cousins house. On Friday she spent the same amount of time driving home. What fraction of day did Sylvia spent driving to her cousin’s house and back? Explain
Answer:
10
Step-by-step explanation:
please help. i'm currently failing !
Answer: it’s a rational number because all rational numbers are fraction, also if you need help on your classes or work I can help you pass okay?
Step-by-step explanation:
Answer:
It has a numerator and denominator
Step-by-step explanation:
Rational number have a numerator and a denominator
1. -3(-2-4-0)+3-(3-5-7)=
Answer: The answer is 18
Answer:
[tex] - 3 + 5 + 7 - 18 + 36 \\ - 3 + 12 - 18 + 36 \\ - 21 + 36 \\ = 15 \: \: \: ans.[/tex]
Can someone help me with this question??
Answer:
-4+12x
Step-by-step explanation:
My teacher likes to give me stuff I haven’t learned
Answer:
haha same
Step-by-step explanation:
i think the answer is B
Answer:
hmm not so difficult
Step-by-step explanation:
I think it's B
need help with geometry
Answer:
20 degrees, 50 degrees, 80 degrees, 75 degrees, 60 degrees
what is x/3=13
please help
Answer:
x=39
Step-by-step explanation:
Z- 6.3 = 2.1
Solve the equation
Answer:
Z = 8.4
Step-by-step explanation:
Jusg move 6.3 behind
When something negative moves behind it becomes positive
So 2.1 plus 6.3 is 8.4
Answer:
Z=8.4
Step-by-step explanation:
1. Add 6.3 to both sides.
Z =2.1+6.3
2.Simplify 2.1+6.3 to 8.4
Z=8.4
--------------------------(Checking answer)
Z−6.3=2.1
1. Let Z=8.4
8.4-6.3=2.1
2. Simplify 8.4-6.3 to 2.1
2.1=2.1
I do not have time to help my sis so help her out ty
Answer:
10.5 Dozens
Step-by-step explanation:
if each gingerbread man has 3, then you will be able to make 126 gingerbread mans, but you asked for dozens, so 126 gingerbread mans divided by 12, which is a dozen, will equal to 10.5 dozens
Brainliest would be appreciated, Thank you.
Consider the graph of the function f(x) = e^x
Answer:
The y intercept is positive 1 because that's where the graph crosses the y axis.
Answer:
Horizontal Asymptote of y= -7
Step-by-step explanation:
Help me and I'll give you all of my points cause I'm leaving the app after this question
Answer:
What’s The question?
Plz answer correctly
Answer:
[tex]7[/tex]
Step-by-step explanation:
This means that there are 20 terms in between 11 and 31
[tex]31-11=20[/tex]
Since we know that the [tex]11th[/tex] term is [tex]29[/tex] and the [tex]31st[/tex] term is [tex]169[/tex], you can subtract the two to find out the values in between
[tex]169-29=140[/tex]
Now all we have to do is divide the values in between by the number of terms to find the common difference.
[tex]\frac{140}{20} =7[/tex]
Therefore the common difference is [tex]7[/tex]
1.) Maria thinks (a + b)² = a² + b². Is she correct? Justify your reasoning.
Answer:
No, Maria is incorrect.
(a+b)^2 is actually equal to a^2 + 2ab + b^2.
Let me know if this helps!
what is the answer to the equation -5+15>-30
Your answer is going to be -20.
Water's strong hydrogen bonds result in which physical properties? Check all that apply.
A. high boiling point
B. low boiling point
C. high specific heat
D. low specific heat
E. density of ice being less than that of liquid water
F. density of ice being greater than that of liquid water
Answer:
1,3,5
Step-by-step explanation:
Got it right
Choose >, <, or = to compare each pair of numbers
6.209 ____ 6.29
Answer:
it would be less than
Step-by-step explanation:
so it would be this <
The magnitude of the number 6.209 is less than the number 6.29 thus the sign of inequality will be < as 6.209 < 6.29.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
Inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given numbers,
6.209 and 6.29
Since, 6.209 - 6.29 = -0.081
Thus, 6.209 < 6.29.
Hence "The magnitude of the number 6.209 is less than the number 6.29 thus the sign of inequality will be < as 6.209 < 6.29".
For more about inequality,
brainly.com/question/20383699
#SPJ3
Give the result of 3(x-2).
Answer:
3x-6
Step-by-step explanation:
3(x-2)
3 multiply both x and -2
3x-6
hope it's helpful ❤❤❤❤
THANK YOU.
a. Cuál es la medida del ángulo R?
P
=37, Q=110°
Which term makes the equation y=sup(x,3)+2x+1 nonlinear?
Answer:
sup(x,3)
Step-by-step explanation:
Linear equation:
A linear equation has the following format:
[tex]y = ax + b[/tex]
In a linear equation, when x changes by 1, y will always change by the amount a, which is called slope.
In this question:
y=sup(x,3)+2x+1
[tex]y = 2x + 1[/tex] would be a linear equation.
However, the expression sup(x,3), that is, the higher value between x and 3, means that the function is not linear.
Which of the following equations correctly represents the law of sines?
Plz I need help this is due at 7:10 and I wasn’t paying attention in class.
Answer:
253cm²
Step-by-step explanation:
Area of the trapezoid = 1/2(b1+b2)*h
Given
h = 22cm
b1 = 10.5cm
b2 = 12.5cm
Substitute
Area of the trapezoid = 1/2(10.5+12.5)*22
Area of the trapezoid = 1/2(23)*22
Area of the trapezoid =11*23
Area of the trapezoid = 253cm²
Hence the area of the trapezoid is 253cm²
[tex]x^{2} +2x=-1[/tex]
how do i solve this with the pq- formula?
Step-by-step explanation:
x²+2x+1
x²+x+x+1
x(x+1)1(x+1).
(x+1)(x+1)
x=-1. , x=-1
Answer:
[tex]\displaystyle \boxed{\text{\sf \Large x=-1}}[/tex]
Step-by-step explanation:
Add 1 to both sides
[tex]x^2+2x+1=0[/tex]
Use quadratic formula with a=1, b=2, c=1
[tex]\displaystyle x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
[tex]\displaystyle x= \frac{-(2) \pm \sqrt{(2)^2-4(1)(1)} }{2(1)}=-1[/tex]
A rectangular garden has a perimeter of 36 yards and a width of 8 yards.
What is the area of the garden?
72 square yards
80 square yards
100 square yards
112 square yards
Answer:
80 square yards
Step-by-step explanation:
We know we have a width of 8 yards and a perimeter of 36.
how I figured it out was:
36=(8*2) * (x*2)
8*2=16
36-16=10
So now we know the length and width.
area of a rectangle is lw (length * width)
10*8=80.
Target is having a holiday sale and is marking down
their entire selection of flat screen TVs. The listed price
of a TV is given at $500 and the sign in front of the TV
says that price is 25% off the listed price. Determine the
marked down price of the TV.
Answer:
$375
Step-by-step explanation:
Convert the 25% discount into a decimal, which is 0.25Multiply the original listed price ($500) by the discount as a decimal (0.25), which is $125Subtract the original list price ($500) by $125 (the discount as a number). This is $375, which is the answer.If y varies directly as x, and y = 7 when x = 3, find y when x = 7
Answer:
AStep-by-step explanation:Direct variation, by definition, has the form shown below:
y=kx
Where k is the constant of proportionality.
Given the information in the problem, you can find k:
7=3k
k=7/3
Now you can find y when x=7 as following:
y=(7/3)x
Substitute values.
y=(7*7)/3
y=49/3
2x + 3x + 5 =
I need the answer asap
Three out of every seven candies sold were chocolate. If 210 candies were sold,
how many were chocolate?
Answer: 90
Step-by-step explanation:
210/7 is 30 times 3 is 90
The basic shipping charge is $10 for the first item via USPS, and $7 more for each additional item. If an equation is made to calculate the shipping charge, what is the slope and y-intercept
.Given the assignment categories and weights listed below, what overall grade should the student get in the class? Round your answer to one decimal place. please show me how you got this and what steps u did please hurry
Weight. Average
Homework30%. 95
Projects 15%. 80
Tests 50% 77
Attendance 5% 50
Answer: The answer of your over all grade is 81
Step-by-step explanation:
You do the % then you add them together.
like in this picture