what is the range of the function f(x)=3x^2+12x + 18

Answers

Answer 1

Answer: {y∈R: y≤6} or [6,∞)

Explanation:

This problem doesn't require too much math. If you look at the equation given, you can see that it is a quadratic equation in the form of[tex]y=Ax^2+Bx+C[/tex]. Since this is a quadratic equation, we have an idea of that the graph would look like. It either curves up or down. Since this is a positive equation, [tex](+3x^2)[/tex], we know that this is going to curve up. In order to find the minimum of the curve, you would use [tex]\frac{-b}{2a}[/tex].

[tex]\frac{-12}{2(3)}=-2[/tex]

This means the x value of the parabola is -2. To find the y, you plug -2 into the  original equation.

[tex]f(2)=3(-2)^2+12(-2)+18[/tex]

[tex]f(2)=6[/tex]

Now that we know the y value of the minimum/vertex is 6, and it is determined that the parabola curves up, the range is y≤6 because the range starts at 6 and goes off toward infinity.


Related Questions

Which of these is most likely an invertebrate? A mushrooms, which are fungi but are often mistaken for plants B oak trees, which belong to the plant kingdom and produce acorns C chimpanzees, which belong to the animal kingdom and related to humans D comb jellies, which belong to the animal kingdom and share many characteristics with jellyfish

Answers

Answer:mushroom

Explanation:i alredy did the qustion before

In a certain Algebra 2 class of 21 students, 12 of them play basketball and 14 of them
play baseball. There are 5 students who play neither sport. What is the probability
that a student chosen randomly from the class plays basketball or baseball?​

Answers

Answer:

Explanation:

We know there are 21 students in all, so that should be the denominator in this answer.

Then, to find the numerator, we need to find the number of students that play basketball and the number of students that play baseball, assuming that none of them play both sports. Just add those two numbers to get the numerator, and then put it on top of the 21.

You either typed this question incorrectly, or there is a mistake, because there are more kids that play basketball or baseball than there are students in the class.

Amit is going to guess on all 20 questions of his multiple-choice test. Each question on the test has 4 answer options, and only one is correct.
Choose 1 answer:

(Choice A)
A
Exactly 5 questions

(Choice B)
B
Close to 5 questions but probably not exactly 555 questions

(Choice C)
C
Exactly 80 questions

(Choice D)
D
Close to 80 questions but probably not exactly 808080 questions

Answers

B ! Close to 5 but not exactly 555 questions

Answer:

Close to 5 but not exactly 5 questions (B)

Explanation:

i got this from maarriiaaaaa. thank you maarriiaaaaa

Also got it correct on Khan   :)

Which areas does acid rain most likely form before rain

Answers

In the clouds
I think

If a/b=1, what is the value of a-b?

Answers

Answer:

0.

Explanation:

If you do a=2 and b=2, then 2-2=0.

a/b=1

If you do a=2 and b=2, then 2-2=0.

a-b=0.

What is the absolute value of the ratio?

If a and b are real numbers then, |-a| = |a| a number and its negative have the same absolute values. |ab| = |a||b| The absolute value of a product is the product of the absolute values. |a/b| = |a|/|b| The absolute value of a ratio is the ratio of the absolute values.

What is the a value in absolute value?

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.

To learn more about a value in absolute value, refer

https://brainly.com/question/12928519

#SPJ2

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