Answer:
Example: <em>- 2x³ + 10x²</em>
Step-by-step explanation:
1.<em>A cubic function</em> is a polynomial of degree 3 in one variable. This means that the highest exponent of the variable is 3: <em>x³</em>
2. <em>Leading coefficient</em> is the coefficient of the term with the highest exponent: in <em>ax³</em> <em>the leading coefficient is a</em>.
3. General form of a <em>cubic function</em>: ax³ + bx² + cx + d, where a ≠ 0
4. <em>Zeros</em> of a polynomial function are the values of x for which the polynomial values zero: <em>ax³ + bx² + cx + d = 0</em>
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5. When the polinomial is factored you can tell easily which the zeros are.
This is how a factored cubic function looks: a(x - x₁)(x - x₂)(x - x₃), where <em>a is the leading coefficient, and x₁, x₂, and x₃ are the three zeroes of the function</em>.
With that, you can write a cubic function with the restrictions stated:
- l<em>eading coefficien of - 2</em>: a = - 2
- <em>one positive zero</em>: x₁ = 5
- for facility, make the other zeros equal to zero, x₂ = 0, and x₃ = 0
- name the function f(x)
result: f(x) = - 2( x -5)(x - 0)(x -0) = -2(x - 5)(x)(x)
- Expand the expression using distributive property:
- 2x³ + 10x²
Answer:
a. f(x)=58-5(x-1); there are 58 boxes in the top row.
b. 273 boxes
Step-by-step explanation:
There are 33 boxes at the bottom row, and there are 5 fewer boxes than the row before it meaning that each row above the bottom row has five more boxes than the one below it.
Basically:
bottom row (with 33 boxes) -->5th row-->4th row-->3rd row-->2nd row-->1st row
each arrow adds five boxes, so if you add 5 boxes for each arrow, there is a total of 58 boxes on the 1st row.
check:
2nd row:
f(x)=58-5(x-1)
f(2)=58-5(2-1)
f(2)=58-5(1)
f(2)=58-5
f(2)=53
and we know that 58 (first row)-5=53 (second row; has to have five fewer boxes) so the function works.
now we can use the formula to find the other row values:
3rd row:
f(x)=58-5(x-1)
f(3)=58-5(3-1)
f(3)=58-5(2)
f(3)=58-10
f(3)=48
4th row:
f(x)=58-5(x-1)
f(4)=58-5(4-1)
f(4)=58-5(3)
f(4)=58-15
f(4)=43
5th row:
f(x)=58-5(x-1)
f(5)=58-5(5-1)
f(5)=58-5(4)
f(5)=58-20
f(5)=38
so, we have the row values from top to bottom:
58, 53, 48, 43, 38, 33
now we just have to add them up, giving us 273 boxes in total.
Sorry I would love to help but I don’t understand
I think you meant y = x^2 + 1. Please use " ^ " to denote exponentiation.
Since you haven't shared the table, I'll choose a few x values and find the corresponding y-values:
x y
-- --
0 1
1 2
2 5
10 101
