Answer:
ax² + bx + c
Step-by-step explanation:
The form of a quadratic equation that is easy to use when finding the maximum or minimum value of the function is ax² + bx + c.
Suppose a quadratic function:
f(x) = 2x² - 8x + 9
Use ( -b/2a , f(-b/2a) ).
-b/2a
a = 2
b = -8
-(-8)/2(2)
8/4
= 2
f(2) = 2(2)² - 8(2) + 9
f(2) = 2(4) - 8(2) + 9
f(2) = 8 - 16 + 9
f(2) = 1
The minimum value of this quadratic function is (2, 1).
It represents a minimum value because a > 0.
3/6 of the beads are purple
3/6 simplified = 1/2
1/2 of 18, or 18/2 = 9
9 beads are purple
hope this helps
Answer:

Step-by-step explanation:
Given
ID Card of 5 digits
Possibly Digits = {0,1...,9}
Required
Probability that a card has exact number 94213
First, we have o determine the total possible number of ID card numbers
Let the card number be represented by ABCDE
Given that repetition of digits is not allowed;
<em>A can be any of 10 digits</em>
<em>B can any of the remaining 9 digits</em>
<em>C can be any of the remaining 8 digits</em>
<em>D can be any of the remaining 7 digits</em>
<em>E can be any of the remaining 6 digits</em>
<em />
Total number of cards = 10 * 9 *8 * 7 * 6
Total = 30240
Provided that the card number is generated at random; each card number has the same probability of 
Hence, the probability of having 94213 is 
Answer:
Fraction of the garden used = 
Step-by-step explanation:
The fifth graders to plant a butterfly garden.
We are given that
Clover grows in ½ of the garden
Daisies grow in ¼ of the garden
Coneflowers grow in ⅛ of the garden
milkweed grows in ⅛ of the garden
The fifth graders notice that the butterflies land on the clover and milkweed.
We are asked to find out the fraction of the garden that the butterflies used.
Fraction of the garden used = clover + milkweed
Fraction of the garden used = 
The LCM of 2 and 8 is 8
Fraction of the garden used = 
Fraction of the garden used = 
Therefore, the butterflies used
fraction of the garden.
Answer: IX - 4I ≤ 4
Step-by-step explanation:
In the numer line we can see that our possible values of x are in the range:
0 ≤ x ≤ 8
And we want to find an absolute value equation such that this set is the set of possible solutions.
An example can be:
IX - 4I ≤ 4
To construct this, we first find the midpoint M of our set, in this case is 4.
Then we write:
Ix - MI ≤ IMI
Notice that i am using the minor and equal sign, this is because the black dots means that the values x = 0 and x = 8 are included, if the dots were empty dots, it would be an open set and we should use the < > signs.