Consider the graph of each quadratic function.(a) Give the domain and range.

Question

Graph of a quadratic function with vertex at (-13, -15) and opening upwards.

Accepted Answer

Hello everybody. I hope you're doing all right. Today, today we're going to be looking at this math question that states find out the domain and range for the graph of the given quadratic function where we have a function that is in parentheses X plus 13 and that parentheses squared and outside of the parentheses minus 15. And then they show us the graph of set quadratic function where the lowest point is between negative 14 and negative 16 at A Y of around negative 15. And then it's a Parabola which extends infinitely upwards. Now the choices are a, a domain of close bracket 15 comma infinity in a range of negative infinity, comma positive infinity. B A domain of negative infinity comma positive infinity and a range of closed bracket comma infinity C A domain of a closed bracket, negative 15 comma positive infinity and a range between negative infinity and positive infinity and D A domain uh between negative infinity and positive infinity and a range between a closed bracket, negative 15 comma positive infinity. No, since they ask us about the domain and the range, we have to think about what each of those entails. So domain will have to do with possible X values of our function. And what does that mean? Well, basically it's going to mean our function extends between what X values. So for we have a quadratic formula and we know that quadratic formulas or quadratic functions have domain between negative infinity and positive infinity. And when you look at the graph that they provided us, you can see why the graph extends upwards. But at the same time, it's getting wider as you go upwards and it's getting infinitely wider. Although it may be getting wider slowly or quick, it is going to be extending infinitely. Therefore, you can go infinitely left and infinitely right. So you have a domain between negative infinity and positive infinity along the X axis or along the XS. So right away, we can eliminate answer choice A and answer choice C because they have a different domain. Now, for the range we're talking about possible. What, why values? So what does this mean? Let's look at our graph, why possible Y values? It's the same idea as the domain. But instead of looking how our graph moves along the X axis, we're trying to see how it moves along the Y axis. In our case, like I mentioned before, we see that the, it's a parabola that has kind of the origin at around A Y of negative 15 and that extends infinitely upwards. It's a parabola is opening upwards with an origin at around negative 15. So we know that our, one of our ranges is gonna be in positive infinity since we're extending infinitely upwards. So we'll have a number comma to positive infinity. Now, that number will be negative 15 because that is where we start. We don't go anywhere below that. So we can't, we won't have for our functions. There are, there are no Y values below negative 15. And in our function specifically that negative 15 is included as part of the graph. It's not an Asy tode, it's not anything that we don't include that negative 15. So because we do that, we do include the negative 15. We used a, we use a closed bracket for that. So a closed bracket means that we include that value as part of our range. So we have a closed bracket negative 15 comma positive infinity to our range. And for example, when you have infinity values, you don't use a closed bracket, you use a simple parentheses because you can't include infinity in your value. Infinity just goes on forever. It's not a solid answer. So that's why you use parentheses for infinity values and for a negative 15, which is included in your graph, you used a close bracket. So those are the domain, you have a domain of negative in of a parentheses, negative infinity comma positive infinity in a range of a closed bracket. Negative 15 2 parent, two positive infinity with the parentheses, which is answer choice. D so I hope that was helpful and until next time.

Consider the graph of each quadratic function.(a) Give the domain and range.

Verified Solution

Key Concepts

Quadratic Functions

Domain and Range

Vertex of a Parabola