Answer:
1) A
2) C
Step-by-step explanation:
Question 1)
We have the function:
[tex]y=2(x+2)^2-3[/tex]
Notice that this is a quadratic function in the vertex form:
[tex]y=a(x-h)^2+k[/tex]
Where (h, k) is the vertex point, a is the leading co-efficient, and h is also the axis of symmetry.
Let's identify these characteristics first. Our leading co-efficient a is 2.
And our vertex is (-2, -3). It is not (2, -3) because (x+2) is the same as (x-(-2)).
We want to find the minimum or maximum value of our function, as well as the domain and range.
First, by looking at our leading co-efficient, which is 2, we can see that it's positive. Therefore, our parabola curves upwards.
Therefore, we will have a minimum value. And this minimum value will be our vertex.
Our vertex is (-2, -3). Therefore, our minimum value is at y=-3.
The domain of all quadratics is always all real numbers.
For the range, we refer to our minimum/maximum value.
Our parabola curves upwards and our minimum value is at y=-3.
Therefore, our range is all numbers greater than or equal to -3.
The choice that represents all of these answers is A.
Question 2)
We have:
[tex]y=2(x+2)^2-4[/tex]
Again, this is in vertex form. Let's identify our characteristics.
Our leading co-efficient a is 2, so the graph curves upwards.
And our vertex is at (-2, -4).
The axis of symmetry is the same as the x-coordinate of our vertex. Therefore, our axis of symmetry is at x=-2.
So, this function has a vertex at (-2, -4) and an axis of symmetry at x=-2.
The choice that represents these characteristics is C.
So, our answer is C.
And we're done!
