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2 years ago

What are the transformations to this quadratic function y= (x+4) power of 2 - 8

Mathematics

1 answer:

I am Lyosha [343]2 years ago

4 0

Answer:

Horizontal shift of 4 units to the left.

Vertical translation of 8 units downward.

Step-by-step explanation:

Given the quadratic function, y = (x + 4)² - 8, which represents the horizontal and vertical translations of the parent graph, y = x²:

The vertex form of the quadratic function is y = a(x - h)² + k

Where:

The vertex is (h , k), which is either the minimum (upward facing graph) or maximum (downward-facing graph).

The axis of symmetry occurs at x = h.

a = determines whether the graph opens up or down, and makes the graph wider or narrower.

h = determines how far left or right the parent function is translated.

k = determines how far up or down the parent function is translated.

Going back to your quadratic function,

y = (x + 4)² - 8

The vertex occrs at (-4, -8)
a is assumed to have a value of 1.
Given the value of h = -4, then it means that the graph shifted horizontally by 4 units to the left.
Since k = -8, then it implies that the graph translated vertically at 8 units downward.

Please mark my answers as the Brainliest, if you find this helpful :)

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Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (w.y) be the unknown

Reil [10]

Answer:

Step-by-step explanation:

Given two coordinates (x₁,x₂) and (y₁,y₂), their midpoint (w,y) is expressed as:

M(X,Y) = $(\dfrac{x_1+w}{2}, \dfrac{y_1+y}{2})$

From the question, we are given the midpoint (X,Y) to be (2,2) and one endpoint as (1, -2) and we are to find the other end point expressed as (w,y). From the coordinates given, i can be seen that X = 2, Y =2, x₁ = 1 and y₁ = -2

Substituting the given end points into the given formula to get the other end points, we will have;

$X = \dfrac{x_1+w}{2} \\2 = \dfrac{1+w}{2} \\cross\ multiply\\4 = 1+w\\w = 4-1\\w = 3$

Similarly;

$Y = \dfrac{y_1+y}{2} \\2 = \dfrac{-2+y}{2} \\cross\ multiply\\4 = -2+y\\y = 4+2\\y = 6$

Hence the other endpoint (w, y) is (3,6)

8 0

3 years ago

A person's height is 5-ft 3-in. Their shadow has a length of 3-ft 6-in. If a nearby tree has a shadow of length 10-ft 4-in, what

Alchen [17]

Answer: The height of tree = 15 ft. 6 inches

Step-by-step explanation:

Given: A person's height is 5-ft 3-in = [5 x (12 )+3 ] inches [ 1 ft= 12 inches]

= 63 inches

Their shadow has a length of 3-ft 6-in = [3 x 12+6] inches

= 42 inches

If a nearby tree has a shadow of length 10-ft 4-in = [10 x 12+4] inches

= 124 inches.

At the same time,

$\dfrac{\text{Height of tree}}{\text{Height of person}}=\dfrac{\text{Length person's shadow}}{\text{Length of tree's shadow}}\\\\\dfrac{\text{Height of tree}}{63}=\dfrac{124}{42}\\\\\Rightarrow\ \text{Height of tree}=\dfrac{124}{42}\times63=186\ inches\\\\=\dfrac{186}{12}= 15.5 ft\ or\ 15 ft.\ 6\ inches.$

Hence, the height of tree = 15 ft. 6 inches

7 0

2 years ago

A handyman is tiling a bathroom l. He needs 34 rows of 18 tiles to cover the floor. How many total tiles does he need to cover t

olchik [2.2K]

Answer:

A handyman need 34 rows of 18 tiles.

How many total tiles does he need?

lets start off by saying that each row has 18 tiles

and there are supposed to be 34 rows

so you can multiply the number of tiles in each row (18) by the number of rows (34)

34 x 18 = 612

the handyman needs a total of 612 tiles to cover the floor.

plz hit the thx button and plz mark me brainliest if this helped :)

3 0

3 years ago

Opal wanted to make some necklaces and sell them at a craft store. She made 37 necklaces and each necklace had somewhere between

alexandr402 [8]

<h3>The total number of beads used in making 37 necklaces is between 2,664 beads and 2,849 beads.</h3>

Step-by-step explanation:

Here, as given: The number of necklace made by Opal = 37

The least number of bead used in each necklace = 72

So, if each necklace is made using the least number of beads then,

The total number of beads used in 37 necklace = 37 x ( beads in 1 necklace)

= 37 x 72 = 2,664 beads

So, the least number of total beads used in 37 necklaces = 2,664 beads

The highest number of bead used in each necklace = 77

So, if each necklace is made using the highest number of beads then,

The total number of beads used in 37 necklace = 37 x ( beads in 1 necklace)

= 37 x 77 = 2,849 beads

So, if highest number of total beads used in 37 necklaces = 2,849 beads

Hence, the total number of beads used in making 37 necklaces is between 2,664 beads and 2,849 beads.

5 0

2 years ago

Write the equation of the line that has a slope of -3/2 and passes through (4, -3)

GREYUIT [131]

Answer:

y = -3/2x + 3

Step-by-step explanation:

y = -3/2x + b

-3 = -3/2(4) + b

-3 = -6 + b

3 = b

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2 years ago