2 answers:
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Answer:
The graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up.
Step-by-step explanation:
The base of the quadratic function is
We can transform this function to look narrower or wider.
Looking narrower is termed a stretch.
This happens when a>1
Looking wider is termed a compression.
This happens when 0<a<1
We can also
+h moves the parent graph to the left by h units
-h moves the parent graph to the left by h units.
+ k moves the parent function up by k units
- k moves the parent function down by k units.
The change that occurs to
given
is that, the graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up
Therefore the last choice is the correct answer.
Answer:
We want to find a solution of the system:
x^2 + y^2 > 49
y ≤ –x^2 – 4
Here we do not have any options, so let's try to find a general solution.
First, we can remember that the equation of a circle centered in the point (a, b) and of radius R is:
(x - a)^2 + (y - b)^2 = R^2
If we look at our first inequality, we can write it as:
x^2 + y^2 > 7^2
So the solutions of the first inequality are all the points that are outside (because the symbol used is >) of the circle of radius R = 7 centered in the origin.
From the other equation, we would get:
y ≤ –x^2 – 4
This is parabola, anything that is in the graph of the parabola or below will be a solution for this inequality.
Then the solutions of the system, are the ones that are in the region of solutions for both inequalities.
You can see the graph below, where both regions are graphed. The intersection of these regions is the region of the solutions for the system of inequalities:
by looking at the graph, we can see a lot of points that are solutions, like:
(0, -10)
(0, -15)
(2, -10)
etc.
