Answer:
Step-by-step explanation:
Given that:
and
If we equate both since they are distances, we have:
Algebraically, moving the equation to the right side, we get:
To factor the equation on the left side:
Factor out 2 on the left-hand side:
To determine the time when the two boats have to cover an equal distance:
Thus:
The true about the domain and the range of the function is:
The domain is all real numbers, and the range is all real numbers
greater than or equal to -4 ⇒ 1st answer
Step-by-step explanation:
f(x) = (x + 2)(x + 6) is a quadratic function with 2 factors (x + 2) and (x + 6)
By multiplying its two factors we will find the form of the quadratic function
∵ (x)(x) = x²
∵ (x)(6) = 6x
∵ (2)(x) = 2x
∵ (2)(6) = 12
∴ f(x) = x² + 6x + 2x + 12
- By adding like terms
∴ f(x) = x² + 8x + 12
The quadratic function represented graphically by a parabola
Look to the attached figure
The x-coordinate of the vertex point of the parabola h =
where b is the coefficient of x and a is the coefficient of x²
∵ f(x) = x² + 8x + 12
∴ a = 1 and b = 8
∴ h =
The y-coordinate of the vertex point is k = f(h)
∵ h = -4
∴ k = f(-4)
∴ k = (-4)² + 8(-4) = 12 = 16 - 32 + 12
∴ k = -4
∴ The vertex point of the parabola is (-4 , -4)
∵ The parabola is opened upward
∴ Its vertex is minimum point
∴ The minimum value of f(x) is y = -4
∵ The domain of the function is the values of x
∵ The range of the function is the values of y corresponding to the
values of x
∵ x can be any real numbers
∴ x ∈ R, where R is the set of real numbers
∴ The domain of f(x) is all real numbers
∵ The minimum value of f(x) is y = -4
∴ y can be any real number greater than or equal to -4
∴ y ≥ -4
∴ The range is all real number greater than or equal to -4
The true about the domain and the range of the function is:
The domain is all real numbers, and the range is all real numbers
greater than or equal to -4
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