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: The person next to you ate more popcorn.
Step-by-step explanation:
3 divided by 4 is 0.75, which is equivalent to 75%. 4 divided by 5 is 0.8, which is equivalent to 80%. Now that you've calculated the percentages of how much they ate, you can assume that 80 > 75 (80 is greater than 75).
Answer:
a recentangle?
Step-by-step explanation:
Answer:
Step-by-step explanation:
abs ( -2(5-(-1)) / 3 )
= abs ( -2(5+1) / 3 )
= abs ( -2(6) /3)
= abs (-12 /3)
= 4
(3(-1) -- 1) /2
= (-3 -1) /2
= -4 / 2
= -2
since 4 is greater than - 2 this is inequality is true
Answer:
18
Step-by-step explanation:
9*2= 18
18-9=9
because it said twice as old as Robin you multiply
Hope this helped you
