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.
Answer:
c
Step-by-step explanation:
I took the test dont worry :)
Answer
-19
Step-by-step explanation:
AS WE NEED TO FIND THE DIFF SO -8-11=-19
six
Step-by-step explanation:
the reason is this: let steak be (s), pork be (p), grilled chicken be (gc), tea be (t), and coffee be (c)
now, we want to find the total number of outcomes, and this cannot be determined by a simple roll of the dice. you have to count the sample space required for EVERY outcome, and it has to lie within the conditions. so, assuming David only takes 1 main course and 1 drink, he would be down to six option, which are :
1. s & t
2. s & c
3. p & t
4. p & c
5. gc & t
6. gc & c
Answer:
5555555555555555555225313
Step-by-step explanation:
3
6
554
