Answers
Given:
The vertex of a quadratic function is (-5,-1) and it passes through the point (-2,2).
To find:
The vertex and standard form of the quadratic function.
Solution:
The vertex form of a quadratic function is:
[tex]f(x)=a(x-h)^2+k[/tex]
Where, a is a constant, (h,k) is vertex.
The vertex of a quadratic function is (-5,-1). It means [tex]h=-5,k=-1[/tex].
[tex]f(x)=a(x-(-5))^2+(-1)[/tex]
[tex]f(x)=a(x+5)^2-1[/tex] ...(i)
The quadratic function passes through the point (-2,2). Putting [tex]x=-2,f(x)=2[/tex] in (i), we get
[tex]2=a(-2+5)^2-1[/tex]
[tex]2+1=a(3)^2[/tex]
[tex]3=9a[/tex]
[tex]\dfrac{1}{3}=a[/tex]
Putting [tex]a=\dfrac{1}{3}[/tex] in (i), we get
[tex]f(x)=\dfrac{1}{3}(x+5)^2-1[/tex]
Therefore, the vertex for of the quadratic function is [tex]f(x)=\dfrac{1}{3}(x+5)^2-1[/tex].
The standard form of a quadratic function is:
[tex]f(x)=Ax^2+Bx+C[/tex]
We have,
[tex]f(x)=\dfrac{1}{3}(x+5)^2-1[/tex]
[tex]f(x)=\dfrac{1}{3}(x^2+10x+25)-1[/tex]
[tex]f(x)=\dfrac{1}{3}x^2+\dfrac{10}{3}x+\dfrac{25}{3}-1[/tex]
[tex]f(x)=\dfrac{1}{3}x^2+\dfrac{10}{3}x+\dfrac{22}{3}[/tex]
Therefore, the standard form of a quadratic function is [tex]f(x)=\dfrac{1}{3}x^2+\dfrac{10}{3}x+\dfrac{22}{3}[/tex].
Related Questions
Use the figure and information below to find the length of each line segment
7th grade math please help me
Answers
Answer:
7. 6
8. 6
9. 12
10. 6
11. 12
12. 24
Step-by-step explanation:
The length of each segment is AB = 6, BC = 6, AC = 12, CD = 6, CE = 12, AE = 24
What is the length?It is the measure of distance between the two points is called a length.
D is the mid-point of CE. Then
CD = DE = 6
B is the mid-point of AC. Then
AB = BC
C is the mid-point of AE. Then
AC = CE
AB + BC = CD + DE
AB + AB = CD + CD
2 AB = 2 CD
AB = CD
AB = 6
Then
AB = 6
BC = AB = 6
AC = AB + BC = 6 + 6 = 12
CD = DE = 6
CE = CD + DE = 6 + 6 = 12
AE = AB + BC + CD + DE = 6 + 6 + 6 + 6 = 24
More about the distance link is given below.
https://brainly.com/question/989117
The rectangle below has an area of 70 square meters.
Find the dimensions of the rectangle.
(x - 11)
(x - 8)
Answers
Answer:
The side lengths are 10 by 7
Step-by-step explanation:
The area of a rectangle is
A = l*w
70 = (x - 11)(x - 8)
FOIL
70 = x^2 -8x-11x+88
Combine like terms
70 = x^2 -19x +88
Subtract 70 from each side
0 = x^2 -19x +88-70
0 = x^2 -19x+18
Factor
What number multiplies to 18 and adds to -19
-18*-1 =18
-18-1 = -19
0=(x-18)(x-1)
Using the zero product property
x-18=0 x-1=0
x=18 x=1
But x cannot x=1 because then the side lengths would be negative
x-18 = 10
x-11 = 7
The side lengths are 10 by 7
John ran 5,000 meters on Monday. He
ran 6 kilometers on Tuesday. How many
total kilometers did John run?
Answers
Answer:
11 kilometers
Step-by-step explanation:
Since there are 1,000 m in 1 km, John ran 5 km on Monday. Combine that with the 6 km he ran on Tuesday, and you get 11 km in total.
Answer:
11 kilometers
Step-by-step explanation:
1000 meters=1 kilometer
5000÷1000=5
5+6=11
3х + 9 < 39
solve the following inequality
Answers
X < 10
Step-by-step explanation:
solve -4 (h - 2) = 8
Answers
Answer:
h=0
Step-by-step explanation:
-4(h-2)=8
/4 /4
h-2=-2
h=0
Hey Btw I strongly reccomend you use photomath for your math classes.
Answer:
[tex] \frac{ - 4(h - 2}{ - 4} = \frac{8}{ - 4} \\ h - 2 = - 2 \\ h - 2 + 2 = - 2 + 2 \\ h = 0[/tex]
-k/3 = 9
answer = ??
Answers
Answer:
-k=9×3
-k=27
God luck friend
help plz!!!!!!!!!!!!!!!!!!!!!
Answers
Explanation:
The equations are
2y=3x
4y=12x
3y= x
y= 3x
pls pls help its due very soon!!
Answers
Answer:
4y+12x
Step-by-step explanation:
I dont have time to type sry
Find the measures of angles 1,2,3,5,6,7, and 8.
Answers
Answer:
1DK
Step-by-step explanation:
Factor 60y - 90 - 20x to identify equivalent expressions
Answers
Answer:
10(6y−9−2x) and 5(12y−18−4x)
Answer: 10(60y/10 - 90/10 +-20x/10)
Your local radio station is having their yearly CD and concert ticket giveaway. For one minute every 4th caller will win a CD and every 7th caller will win a concert ticket. You were the second caller to win both a CD and a concert ticket. What number caller were you?
Answers
Answer:
i was number #173
Step-by-step explanation:
Answer:
56
Step-by-step explanation:
You have to find the lcm, and that is 56! Hope that helps.
write the expression below in simplest form. 3x^2 + 8x -1+2(x^2 +5x+3) (work shown please!)
Answers
Answer:
5x^2+18x+5
Step-by-step explanation:
Answer:
5x² + 18x + 5
Step-by-step explanation:
Given
3x² + 8x - 1 + 2(x² + 5x + 3) ← distribute parenthesis
= 3x² + 8x - 1 + 2x² + 10x + 6 ← collect like terms
= 5x² + 18x + 5
Evaluate the Expression when x = 6 and y = 5.
(x - 1) + (y - 1)
Answers
Answer:
9
Step-by-step explanation:
What is the surface area of the triangular prism?
A. 13 in.2
B. 36 in.2
C. 78 in.2
D. 84 in.2
Answers
I'm marking brainiest if you help me :)
Answers
Answer:
the possible line of best fit equation is;
y = 10x + 24
Step-by-step explanation:
Here, we want to get the approximate line of best fit
Mathematically, we have the general line of best fit as
y = mx + b
where m is the slope and b is the y-intercept
By joining the given lines, we can see that the y-intercept values fall a little below 30
This means that the possible y-intercept value is 24
Now, to get the slope value, we select any two points and use the slope equation
We can have (3,50) and (6,80)
Using the slope equation;
m = (y2-y1)/(x2-x1) = (80-50)/(6-3) = 30/3 = 10
The equation is thus;
y = 10x + 24
Allison invested $70,000 in an account paying an interest rate of 6.2%
compounded continuously. Assuming no deposits or withdrawals are made,
how long would it take, to the nearest year, for the value of the account to
reach $223,200?
Answers
Answer: 19
Step-by-step explanation: j trust me
1 MATH PROBLEM POINTS + BRAINIEST
Answers
The length of a rectangle is one inch less than three times its width. If the perimeter of the rectangle is 118 inches, find the dimensions of the rectangle.
Answers
3. Solve for the side length of BA and AC. * (image attached)
1 point
Captionless Image
BA = 8, BA = 30
BA = 8, AC = 16
BA = 8, AC = 8√2
BA = 8, AC = 8√3
Answers
Answer:
D. BA = 8, AC = 8√3
Step-by-step explanation:
First, because this is a right triangle, refer to the trigonometric ratios:
tangent = opposite side/adjacent side
sine = opposite side/hypotenuse
cosine = adjacent side/hypotenuse
BA is the opposite side to the angle measure given, ∠C—which is 30°—and we have the measure of BC. BC is the hypotenuse, as it is across from the right angle of the right triangle. So we can use sine:
sine = opposite side/hypotenuse
sin(30) = BA/16
sin(30) / 1 = BA / 16
Cross multiply:
BA = sin(30) (16)
BA = 8
AC is the adjacent side to the angle measure given, ∠C—which is 30°—and we have the measure of BC. BC is the hypotenuse, as it is across from the right angle of the right triangle. So we can use cosine:
cosine = adjacent side/hypotenuse
cos(30) = AC/16
cos(30) / 1 = AC / 16
Cross multiply:
AC = cos(30) (16)
AC = 8√3
You can check by using the Pythagorean Theorem:
a² + b² = c²
8² + (8√3)² = 16²
64 + 192 = 256
256 = 256
Please help!!!!
Order these numbers from least to greatest.
6.1, 6.22, 6.202, 6.1021
Answers
Answer:
well played ahajkdjajkskdjdhdjskkskfjsiiskfks
Which shape has 3 sides and 3 corners?
Answers
PLEASE I NEED HELP ASAP
In diagram triangle PQV and triangle WXY . What is length of XY
Answers
Answer:
:(
Step-by-step explanation:
idek
What is 74% of 44.I appreciate your help
Answers
Answer:
32.56
Step-by-step explanation:
Hi there i need help in this
1 (-23) + (-15) =
2 12 + 24 =
3 (-28) + (-16) =
4 15 + 29 =
5 29 + (-13) =
6 (-14) + (-10) =
7 + (-20) =
8 (-21) + 19 =
9 11 + (-20) =
10 24 + (-6) =
11 28 + 15 =
12 23 + (-19) =
pls are negative and positive numbers
Answers
Answer:
1.-38
2.36
3.-44
4.44
5.16
6.-24
7.?
8.-2
9.-9
10.18
11.43
12.4
Step-by-step explanation:
lol have a good day!
For each function shown:
*Name the starting point.
*Explain how y changes as x increases.
Function #1: [tex]y = 0.5 + 3x[/tex]
Function #2: [tex]y = 3(5)^x[/tex]
Answers
Answer:
The starting point of
F1 is
[tex](0. \frac{1}{2} )[/tex]
F2 is
[tex](0.3)[/tex]
Y will increase if the x increase in the two equation
Step-by-step explanation:
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the graphs below have the same shape. what is the equation o the red graph?
Answers
So the equation of the red graph is already given to us: [tex]f(x) = x^2[/tex]. I assume you meant the blue graph?
We can use the vertex form: [tex]y = a(x - h)^2+ k[/tex], where [tex](h,k)[/tex] is the vertex. (We can ignore [tex]a[/tex] because [tex]a[/tex] is 1 for this graph.) Remember that the vertex is the maximum or minimum of a parabola and the point that the line of symmetry passes through. For f(x) the vertex is (0,0).
The vertex for [tex]g(x)[/tex] is at [tex](-4, -2)[/tex] on the coordinate plane. (4 left, 2 down)
Plug into the vertex form:
[tex]y = (x - (-4))^2 -2[/tex]
The double negative becomes a positive, and then you're done:
[tex]y = (x + 4)^2-2[/tex]
The length of a rectangle is triple the width. The perimeter is 54 m. Find the dimensions of the rectangle
Answers
Answer:
W = 6.75
L = 20.25
Step-by-step explanation:
2(w + 3w) = 54
8w = 54
w = 6.75
L = 20.25
f(x) = x2. What is g(x)?
Answers
Answer:
Step-by-step explanation:
x-2
What’s the slope m and y-intercept b of both these images?
Answers
Answer:
Slope = 1
y-intercept = 3
Step-by-step explanation:
Since, slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through two points (0, 3) and (-3, 0) will be,
Slope = [tex]\frac{3-0}{0-(-3)}[/tex]
Slope = 1
y-intercept of the line = distance between the origin and point of intersection of the line with y-axis
y-intercept = 3
What is 16 – x at x = 5?
Answers
Answer:
11
Step-by-step explanation:
16-x
substitute with 5
16-5
11
The value is 11.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Here, given that,
16-x
now, we have to ,
substitute with 5
=16-5
=11
Hence, The value is 11.
To learn more on subtraction click:
brainly.com/question/2346316
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