1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mestny [16]
3 years ago
14

HELP 40 POINTS

Mathematics
1 answer:
Tom [10]3 years ago
7 0
Answer: the function g(x) has the smallest minimum y-value.


Explanation:


1) The function f(x) = 3x² + 12x + 16 is a parabola.


The vertex of the parabola is the minimum or maximum on the parabola.


If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.


The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.


When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).


Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.


Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).


Then the minimum value is 4 (when x = - 2).


2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>

The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.


When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2


Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

You might be interested in
GIVING BRAINLY IF CORRECT
Hatshy [7]
Do you have a picture ? If so , you should upload it .
4 0
2 years ago
Please help me.. I need the answer quick..
user100 [1]
What answer do you need it for
3 0
3 years ago
What is the length of the arc that subtends a central angle of 139°, for a circle with a radius of 7.5 centimeters? Use 3.14 for
eduard
18.19 139/360=x/diameter 
7 0
3 years ago
Read 2 more answers
The amount of paper needed to cover a Vic too in the shape of a trapezoid is 198cm squared.If the height of the bud too is 18 ca
Jlenok [28]
The length of the other base is 82
4 0
3 years ago
How many 2/3 ounce portions of chocolate can Anna get from the 42/3 ounces of chocolate she bought at Union Market?
Lelechka [254]
She can get 21 portions. Since 2/3 and 42/3 already share the same denominator, all you need to do is divide 42 by 2 to get 21.
6 0
3 years ago
Other questions:
  • Perpendicular to y = 3x + 4 through (0, -2)
    5·1 answer
  • PLS HELP ME ASAP
    8·1 answer
  • a grain of sand has a mass of approxlmently 6 x 10^-2 grams. earth has a mass of approximately 6 x 10^28 grams. hiw many times s
    11·2 answers
  • What is 42 divided by 8610
    5·2 answers
  • I NEED HELP<br><br><br>IM NO GOOD AT RATES<br>I CANT GO ONE TILL THIS IS ANSWER
    11·2 answers
  • Find g(f(x)) when f(x) = 3x2 + x - 8, and g(x) = 4x + 5.
    9·1 answer
  • Can anyone help me please
    7·1 answer
  • 38 − 7x = −2(x − 29)
    15·2 answers
  • Can I have some help with this? Construct a linear function that has a slope of -3 and passes through the point (-2,3).
    10·1 answer
  • Burton wants to rent a bike to go trick-or-treating so he can get to more houses. One place he
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!