Please help me with this math assignment!
1 answer:
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Answer:
(A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6
(B) f(x + h) - f(x) = 8xh + 4h² - 6h
(C)
Step-by-step explanation:
* Lets explain how to solve the problem
- The function f(x) = 4x² - 6x + 6
- To find f(x + h) substitute x in the function by (x + h)
∵ f(x) = 4x² - 6x + 6
∴ f(x + h) = 4(x + h)² - 6(x + h) + 6
- Lets simplify 4(x + h)²
∵ (x + h)² = (x)(x) + 2(x)(h) + (h)(h) = x² + 2xh + h²
∴ 4(x + h)² = 4(x² + 2xh + h²) = 4x² + 8xh + 4h²
- Lets simplify 6(x + h)
∵ 6(x + h) = 6(x) + 6(h)
∴ 6(x + h) = 6x + 6h
∴ f(x + h) = 4x² + 8xh + 4h² - (6x + 6h) + 6
- Remember (-)(+) = (-)
∴ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6
* (A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6
- Lets find f(x + h) - f(x)
∵ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6
∵ f(x) = 4x² - 6x + 6
∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - (4x² - 6x + 6)
- Remember (-)(-) = (+)
∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - 4x² + 6x - 6
- Simplify by adding the like terms
∴ f(x + h) - f(x) = (4x² - 4x²) + 8xh + 4h² + (- 6x + 6x) - 6h + (6 - 6)
∴ f(x + h) - f(x) = 8xh + 4h² - 6h
* (B) f(x + h) - f(x) = 8xh + 4h² - 6h
- Lets find
∵ f(x + h) - f(x) = 8xh + 4h² - 6h
∴
- Simplify by separate the three terms
∴
∴
* (C)
Answer:
The coordinates of the point b are:
b(x₂, y₂) = (-5, -1)
Step-by-step explanation:
Given
As m is the midpoint, so
m(x, y) = m (-7, -2.5)
The other point a is given by
a(x₁, y₁) = a(-9, -4)
To determine
We need to determine the coordinates of the point b
= ?
Using the midpoint formula
substituting (x, y) = (-7, -2.5), (x₁, y₁) = (-9, -4)
Thus equvating,
Determining the x-coordinate of b
[x₂ + (-9)] / 2 = -7
x₂ + (-9) = -14
x₂ - 9 = -14
adding 9 to both sides
x₂ - 9 + 9 = -14 + 9
x₂ = -5
Determining the y-coordinate of b
[y₂ + (-4)] / 2 = -2.5
y₂ + (-4) = -2.5(2)
y₂ - 4 = -5
adding 4 to both sides
y₂ - 4 + 4 = -5 + 4
y₂ = -1
Therefore, the coordinates of the point b are:
b(x₂, y₂) = (-5, -1)