Hello,
You have to know this property:
You have to know this property:
Please help! Will give all my points! Due in 30 mins!
1 answer:
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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
Learn more:
You can learn more about quadratic function in brainly.com/question/1332667
#LearnwithBrainly
Answer:
A) 8, 15, 17.
Step-by-step explanation:
Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option (the hypotenuse) that means that those numbers could be the sides of a right triangle.
The Pythagorean theorem states that:
Thus:
Option A:
→ 17 = 17 OK!
Option B:
→ 10 ≠ 12 NO
Option C:
[/tex] →
≠ 21 NO
Option D:
→
≠ 16 NO