how to graph transformations of quadratic functions
Answer:
Shift "h" units to the right, "k" units up, and reflect over the x or y axis when needed.
Step-by-step explanation:
1) I want to talk about reflections first.
Reflections across the x-axis --> [tex]y = ax^2[/tex], a is the coefficient. if a is negative, then the equation should be reflected across the x-axis. This is known as a vertical reflection. Reflections across the y-axis --> [tex]y=a(bx)^2[/tex], b is the coefficient. If b is negative, then reflect the equation over the y-axis. There are cases where the reflection across the y-axis does not change anything. But, let's say its [tex]y=(x-3)^2[/tex]... the reflection across the y-axis is different (that equation is: [tex]y=(-x-3)^2[/tex] )2) Rigid transformations
Horizontal transformations (to the left or right): [tex]y=a(bx-h)^2[/tex], factor out b from "bx-h" and whatever h equals is the units to the right. If h is a negative number, then you move to the left. Vertical transformations (up and down): [tex]y = a(bx-h)^2+k[/tex]... k is just the units up... if k is negative then we move it down.Example (check image for visual)
We transform [tex]y = x^2[/tex] to [tex]y = -(-x-3)^2+3[/tex] , you move right 3, then reflect across the x-axis, then reflect across y-axis, then move 3 up.
--------------------------------------------------------------------------------------------------------------
Note: In the image, the red line is the original function, the blue one is the transformed function. See if you can follow along with the verbal instructions I gave above.
State the slope and y-intercept for the graph of
- 8x + y = -12.
Answer:
y must have a numerical coefficient of 1. This equation does. If it does not, then you must divide through by whatever is in front of the y.
To read the slope, you must have x and its coefficient on opposite sides of the equal sign.
So you get
y = 8x – 12 when you add 8x to both sides
Next, the y intercept is found when x = 0
y = 8x – 12
y = 8(0) – 12
y = – 12
The y intercept is -12 or in point form (0, – 12)
Answer
slope = 8
y intercept = – 12
Step-by-step explanation:
Please help guys this is just domain and range
Answer:
domain: x>=0
range: y>=1
Step-by-step explanation:
domain: x>=0
range: y>=1
The quadratic function g(x)=ax^2+bx+c has the complex roots (-5+9i) and (-5-9i).
What is the value of a?
What is the value of b?
What is the value of c?
Answer:
I don't know sorry
I need help to find the radius
Answer:
Step-by-step explanation:
i think 0.6
A scale drawing of a rectangular park had a scale of 1 cm = 100 m. What is the actual perimeter of the park in meters?
10.1 and 8.8
Answer:
3780 m
Step-by-step explanation:
First, we find the perimeter of the scale drawing.
perimeter = 2(L + W)
perimeter = 2(10.1 cm + 8.8 cm)
perimeter = 2(18.9 cm)
perimeter = 37.8 cm
Now that we have the perimeter of the drawing, we use the scale to find the real perimeter.
1 cm (drawing) = 100 m (real)
37.8 cm × 100 m/cm = 3780 m
Answer: 3780 m
Please help me asap
ty :)
Answer:
y = -3x - 3
Step-by-step explanation:
Subtract 3x both sides
y = -3 - 3x
y = -3x + (-3)
triangle abc has an area of 6 and a perimeter of 12. if the triangle is dilated by a scale factor of 3 centered at the origin, what is the area and perimeter of its image, triangle a'b'c'?
Answer:
perimeter: 36 unitsarea: 54 square unitsStep-by-step explanation:
The perimeter is multiplied by the scale factor:
image perimeter = 3 × original perimeter = 3×12 = 36 units
The area is multiplied by the square of the scale factor:
image area = 3² × original area = 9×6 = 54 square units
Can someone please help me!!?
Answer:
Step-by-step explanation:
Domain is all the x's on the graph. The graph does go from -3 to 4 (not including the -3 but including the 4). Pay attention to the use of () as well as [] on the answers. Those answers are not weird coordinates, they are intervals where the first number is the starting place and the second number is the end. Also on the graph one end point is an open circle which means it's not included on the graph and the other endpoint is a darkened circle which means it is included. The range is all the y's. It does go from -3 to 3. Increasing means the graph is going up from left to right and decreasing means the graph is going down left to right. The graph is positive when it is above the x-axis and negative when its below the x-axis. It seems like ALL of the statements about the graph are true.
2(t+1)=10
t= ? ............................................
Answer:
4
Step-by-step explanation:
2x5=10
5-1=4
2(4+1)=10
3 ½ pints = ___ cups
Answer:
8.40665 cups
Step-by-step explanation:
hope this is helpful!
HELP HURRY PLS
Graph y= 1/2x-3
Answer:
This is what it would look like. Hope this helps!
Find the sum of all solutions to the equation $3x(x+4) = 135$.
Answer:
-4
Step-by-step explanation:
3x(x + 4) = 135
3x² + 12x = 135
3x² + 12x - 135 = 0
On dividing by 3
x² + 4x - 45 = 0
x² + (9x - 5x) - 45 = 0
x² + 9x - 5x - 45 = 0
x(x + 9) - 5(x + 9) = 0
(x + 9)(x - 5) = 0
x = 5 & -9
Sum = -9 + 5
Sum = -4
The sum of the solutions of the given quadratic equation will be -4.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
As per the given equation,
⇒ 3x(x + 4) = 135
Multiply the 3x as,
3x² + 12x = 135
3x² + 12x - 135 = 0
Divide the above equation by 3 as
3x²/3 + 12x/3 - 135/3 = 0
x² + 4x - 45 = 0
x² + 9x - 5x - 45 = 0
x(x + 9) - 5(x + 9) = 0
(x - 5)(x + 9) = 0
x = 5 and x = -9
Therefore the sum will be -9 + 5 = -4
Hence "The total of the quadratic equation's answers will be -4".
For more about the quadratic equation,
https://brainly.com/question/17177510
#SPJ2
100
O () = 97 +18
or()- +2
x= +
OF (x) = 97 +2
F(x) = -27 + -
10
Answer:
9x+2
Step-by-step explanation:
the inverse of the function is the opposite. 1/9 becomes 9 and negative 2 becomes positive 2
Answer:
first option
Step-by-step explanation:
let y = f(x) and rearrange making x the subject
y = [tex]\frac{1}{9}[/tex] x - 2 ( add 2 to both sides )
y + 2 = [tex]\frac{1}{9}[/tex] x ( multiply through by 9 to clear the fraction )
9y + 18 = x
change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then
[tex]f^{-1}[/tex] (x) = 9x + 18
identify the median of 15-18
solve this to pretty pretty pls
Answer:
3) 161
Step-by-step explanation:
Indeed this is pretty easy :D
What we need to find is the surface area of the rectangular prism excluding the area of the hole. First, let's find out the width of the box, we can do this by using the area, the length, and the height, and we can write:
[tex]V=lhw[/tex]
(Formula to find the volume of a rectangular prism)
[tex]140=(4)(7)w\\ 140=28w\\ 5=w[/tex]
Now that we have the width, can find the area of the top part of the prism:
[tex](5)(4)=20[/tex]
The area of the top part of the prism is 20, and the circle has 1/4 of the area of that:
[tex]A_{circle} = \frac{A_{top part} }{4}\\ A_{circle} = \frac{20}{4} \\ A_{circle} = 5[/tex]
So the area of the circle is 5. Now we just need to find the surface area of the rectangular prism and subtract that result with the area of the circle:
[tex]A_{circle}=5\\ SA_{rec.pri.}=2(lh+lw+wh)\\ SA_{rec.pri.}=2((4)(7)+(4)(5)+(5)(7))\\ SA_{rec.pri.}=2(28+20+35)\\ SA_{rec.pri.}=2(83)\\ SA_{rec.pri.}=166[/tex]
Subtract these two results...:
[tex]166-5=161[/tex]
And we are done!
Brady rode his bike 70 miles in 4 hours. He rode at an average speed of 17 mph for t hours and alah
respeed of 22 mph for the rest of the time. How long did Brady
ride at the slower speed? Use the variablet to
represent the time, in hours, Brady rode at 17 mph.
Answer:66 slower speed
Step-by-step explanation:
Given the two similar triangles below, which proportion is true?
Answer:
B) 10/15 = 15/22.5
Step-by-step explanation:
For the two triangles, proportions that involve ratios of the corresponding sides are true.
A store owner bought 15001500 pencils at \$0.10$0.10 each. If he sells them for \$0.25$0.25 each, how many of them must he sell to make a profit of exactly \$100.00$100.00
Based on the information given, the number of pencils that should be sold will be 1000 pencils.
Let the number that should be sold be x.
A store owner bought 1500 pencils at $0.10 each. Therefore, the cost price will be:
= 1500 × $0.10 = $150
Profit = Selling price - Cost price
100 = 0.25x - 150
0.25x = 100 + 150
0.25x = 250
x = 250/0.25
x = 1000
Therefore, 1000 pencils should be sold.
Learn more about equations on:
https://brainly.com/question/13802812
Can someone explain how to do this:
If you put 10 in to the function f(x) = 2x, what would be the output?
--
Im so lost-
Answer:
It would be 2 (10)
Step-by-step explanation:
If you replace x with 10 then you have a multiplacation problem and the output of the answer is 20
Angelique Calculated the slope of a line that passed through points (-5,4) and (2,-3) her work is shown below. identify her error and correct her mistakes.
Answer:
see explanation
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 4 ) and (x₂, y₂ ) = (2, - 3 )
m = [tex]\frac{-3-4}{2-(-5)}[/tex]
Her error was subtracting 5 from 2 instead of - 5 from 2
m = [tex]\frac{-7}{2+5}[/tex] = [tex]\frac{-7}{7}[/tex] = - 1 ← corrected solution
(Help me please!!)
Write the equation of each linear relationship in slope-intercept form. (Convert the slope to decimal form.)
X: 25, 35, 45, 55
Y: 94. 88, 82, 76
Answer:
y = -0.6x +109
Step-by-step explanation:
The slope is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (88 -94)/(35 -25) = -6/10 = -0.6
The y-intercept is ...
b = y -mx = 94 -(-0.6)(25) = 109
The equation of the line is ...
y = mx +b
y = -0.6x +109
‼️DUE TODAY‼️
(Question in the picture)
Answer:
I Don't know
Step-by-step explanation:
I don't know I don't know I don't know
The diagram shows a map of three land masses, numbered region 1, region 2, and region 3, connected via bridges over water. Each bridge can be traversed in either direction. (diagram is attached)
Show that there are 10 walking routes that start and end in region 2, crossing over water exactly twice. Assume each bridge, when crossed, is fully traversed to the next land mass.
Answer:
Explanation
Step-by-step explanation:
If you look closely, every route connected to region 2 could go to either region 1 or 3, which each could go back to region 2 in 3 different formats. For example the top bridge of region 2, could go through region 1, then region 3 then to the middle bridge of region 2. This can happen for all three of the other route when going backs and works for all bridges in region 2.
in a sale there is a 40% discount.what is the discount on a dress that costs $150.00
Answer:
$90 or $60
Step-by-step explanation:
2(x-3) < 3(2x+2)
How do I solve for x
Answer:
x < -3
Step-by-step explanation:
2(x-3) < 3(2x+2)
Use the distributive property.
(2× x)-(2×3) < (3 × 2x) + (3×2)
2x-6 < 6x+6
add 6 to both sides
2x < 6x+12
subtract 6x from both sides.
-4x < 12
divide both sides by -4
x < -3
A cylinder has a height of 4 centimeters. Its volume is 12.56 cubic centimeters. What is the radius of the cylinder?
Step-by-step explanation:
hope it will help you...
Answer:
radius of cylinder = 1 cm
Step-by-step explanation:
Start with the formula for the volume of a cylinder: V = (pi)r²h, where r is the radius and h is the height. We want to solve this for the radius, r.
Dividing both sides of the Volume formula (above) by (pi)h, we get:
V
r² = -----------
(pi)h
If we now substitute 12.56 cc for V, 3.14 for pi and 4 cm for h, we get:
V 12.56 cc
r² = ---------- = ----------------- = 1 cm²
(pi)h 3.14(4 cm)
Taking the square root of both sides, we get r = 1 cm
Please help me Find the slope no links or bots please and thank you I really need help
Answer:
B) -7/4
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Identify.
y = -7/4x + 4
Step 2: Break
Slope m = -7/4
y-intercept b = 4
Given that AABCDEF, solve for X.
B
A. 10
o
B. 6
C. 17
0 0
Answer:
D
Step-by-step explanation:
Given Δ ABC is similar to Δ DEF then the ratios of corresponding sides are in proportion, that is
[tex]\frac{EF}{BC}[/tex] = [tex]\frac{DE}{AB}[/tex] , substitute values
[tex]\frac{x}{42}[/tex] = [tex]\frac{5}{30}[/tex] ( cross- multiply )
30x = 5 × 42 = 210 ( divide both sides by 30 )
x = 7
The ratio remains same
[tex]\\ \sf\dashrightarrow \dfrac{5}{x}=\dfrac{30}{42}[/tex]
[tex]\\ \sf\dashrightarrow \dfrac{5}{x}=\dfrac{15}{21}[/tex]
[tex]\\ \sf\dashrightarrow 15x=105[/tex]
[tex]\\ \sf\dashrightarrow x=7[/tex]
In a lab experiment, 5300 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 23 hours. How long would it be, to
the nearest tenth of an hour, until there are 10500 bacteria present?
Answer: x = 22.7
Step-by-step explanation:Based on the given conditions, formulate: 5300x2(x divided by 23) = 10500
Divide both sides of the equation by the coefficient of variable: 2 x/23 = 10500/5300
Reduce the fraction:2 x/23 = 105/53
Convert exponential to logarithm form: x/23 = long^2 105/53
Divide both sides of the equation by the coefficient of variable:x = log^2 105/53 x 23
Rewrite the expression: x = 23 long^2 105/53
Round the number: x = 22.7
Answer: x = 22.7