Answer:
f(-3) = -20
Step-by-step explanation:
We observe that the given x-values are 3 units apart, and that the x-value we're concerned with is also 3 units from the first of those given. So, a simple way to work this is to consider the sequence for x = 6, 3, 0, -3. The corresponding sequence of f(x) values is ...
34, 10, -8, ?
The first differences of these numbers are ...
10 -34 = -24
-8 -10 = -18
And the second difference is ...
-18 -(-24) = 6
For a quadratic function, second differences are constant. This means the next first-difference will be ...
? -(-8) = -18 +6
? = -12 -8 = -20
The value of the function at x=-3 is -20.
_____
The attachment shows using a graphing calculator to do a quadratic regression on the given points. The graph can then be used to find the point of interest. There are algebraic ways to do this, too, but they are somewhat more complicated than the 5 addition/subtraction operations we needed to find the solution. (Had the required x-value been different, we might have chosen a different approach.)
The following are the answers to
the questions presented:
Part 1:
Vertex: <span>(<span><span>−3</span>/ 2</span>,<span> 11/2</span>)</span>
Axis of
symmetry = x = -3/2
Domain = all
real numbers
Range = <span>y </span><span>≤ </span>11/2
Part 2:
A quadratic equation is symmetrical around its vertex. The
equation for the axis of symmetry is x = -3/2 since the equation is in terms of
x. Since no value of x is undefined, then the domain of the equation is clearly
all real numbers. Since the value of “a” is negative, then that means the y
coordinate of the vertex is the maximum value so the range will never get above
11/2. I am hoping that these answers have satisfied your queries and it
will be able to help you in your endeavors, and if you would like, feel free to
ask another question.
<span>Complete the following direct proof.
1) Triangles are the only polygons with three sides.
2) The polygon has three sides.
3) Thus, triangles are polygons.
</span>
This is a word problem for 12.
Laura decided to throw a party. The DJ charged 2 dollars an hour and 4 dollars to use lights and fog. How long did the DJ play?
This one is for 11.
Kate wanted to go skating. When she got there it was 4 dollars an hour. The total cost was 12 dollars. How many hours did she skate?
Answer: D.Hormones
Step-by-step explanation:
