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 <u>minimum</u> (upward facing graph) or <u>maximum</u> (downward-facing graph).
The axis of symmetry occurs at <em>x = h</em>.
<em>a</em> = determines whether the graph opens up or down, and makes the graph wider or narrower.
<em>h</em> = determines how far left or right the parent function is translated.
<em>k</em> = 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 <em>h</em> = -4, then it means that the graph shifted horizontally by <u>4 units to the left</u>.
- Since k = -8, then it implies that the graph translated vertically at <u>8 units downward</u>.
Please mark my answers as the Brainliest, if you find this helpful :)
To find this answer, we should subtract 2 1/2 from 3 1/4. The simplest way to do this is to turn them into improper fractions, found the least common denominator, and subtract the numerators.
3 1/4=13/4
2 1/2=5/2
The least common multiple is 4, so we should multiply the numerator and denominator of 5/2 by 2.
5/2=10/4
Now we can just subtract the numerators.
13/4-10/4=3/4
Using the math above, we can see that it saves D. 3/4 hours.
720 by 600! hope this helps
Answer:
The decrease was $1755.
At the end of the year, he had $6045 in his account.
Step-by-step explanation:
Start with $7800.
Decrease of 22.5% of $7800.
22.5% of $7800 =
= $1755
The decrease was $1755.
$7800 - $1755 = $6045
At the end of the year, he had $6045 in his account.
Answer:
There are 6 coins in nickels and 9 coins in quarters.
Step-by-step explanation:
Now, to find the solution.
According to question:
The number of nickels = 
.
The number of quarters = 
So, the total number of coins:
He had 3 more quarters than nickels.
Thus,
.....(1)
Now, to get the solution:
Substituting the equation (1):
<em>Subtracting both sides by 3 we get:</em>
<em />
<em />
<em>Dividing both sides by 2 we get:</em>
<em>The number of nickels = 6.</em>
Now, substituting the value of in equation (1):
<em>The number of quarters = 9.</em>
Thus, there are 6 coins in nickels and 9 coins in quarters.
