Answer:
, which corresponds to answer D.
Step-by-step explanation:
Recall that the maximum or minimum of a parabola is always located at its vertex. Notice that all quadratic functions listed are given in what is called "vertex" form, since they explicitly show the vertex coordinates in their formulation:
where 
, and 
stand for the x and y coordinates respectively of the vertex.
Examining all four options, we notice that in all four cases listed, the is correct (equal to positive 9), so we proceed to examine what the 
expression should look like for 
:
Notice that when replace with "-3", we end up with a sign change:
Therefore we find that the last two options can be candidates. Then we recall that the question also states that this should be a minimum. Then, for a parabola to have a minimum, its branches must go upwards, and this corresponds to a case in which the factor 
(leading coefficient) multiplying (x-x_v)^2 is positive. So in looking for such condition, we find that the very last option is the only one that verifies such.
Then, is the option we select.
Answer:
x=-3 and x=0
Step-by-step explanation:
The values where f(x) = g(x) is where the graphs intersect
One point is at (-3,0) and the other point is at (0,6)
We have two points of intersection since one is a parabola and the other is a line
Step-by-step explanation:
n-8≤17
add 8 on both sides to isolate the variable.
n is less than or equal to 25
No two <em>intergers</em> can solve this problem. If you're not in Algebra II yet, the answer is probably "none."
Just look at the factor pairs of 25:
1 × 25
-1 × 25
5 × 5
-5 × -5
Clearly none of those can add up to 6.
If you want the more complex answer, I'll show you how here. If you don't understand why it doesn't work, that's okay. I just want you to see that there's not an actual answer to the problem.
a+b = 6
a = 6-b
ab = 25
(6-b)b = 25
6b -b² = 25
-b² + 6b = 25
b² -6b = -25
Factor by splitting the middle.
Half of -6 is -3, (-3)² = 9. Add this to each side.
b² -6b + 9 = -16
Factor the perfect square trinomial.
(b-3)² = -16
Take the square root of each side.
b-3 = 4i
b = 3+4i
a+b = 6
a+3+4i = 6
a= 3-4i
<em>(The "i" stands for an imaginary number, specifically, the square root of -1.)</em>
Answer:
NO! The correct answer is 2.03 (where 3 is repeating)
Step-by-step explanation:
0.2 + 12 / (1.5*4) does not equal 32.04
Parenthesis first! 1.5 times 4 equals 6.
0.2 + 12 = 12.2
12.2/6
12.2/6= 2.0333... but it should be rounded to 2, because
