Question

Need these 2 answered. 50 points! Please Show your work, Thanks! :)

Answer 1

Answer:

1) A

2) C

Step-by-step explanation:

Question 1)

We have the function:

$y=2(x+2)^2-3$

Notice that this is a quadratic function in the vertex form:

$y=a(x-h)^2+k$

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:

$y=2(x+2)^2-4$

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!