In Exercises 45–48, give the domain and the range of each quadrat...

Question

In Exercises 45–48, give the domain and the range of each quadratic function whose graph is described. The vertex is and the parabola opens up.

Accepted Answer

everyone here we are asked to find the domain and range of the parabola which opens up and has a vertex of negative five negative six. Now, here let's first recall the vertex form of a parabola which is F of X. Is equal to a times a quantity of x minus H squared plus K. And now here, since we know the Parabola opens up, we know that this a value must be positive. So we can say that A. Is greater than zero and with a being greater than zero we know that the parabola has a minimum value. So to better visualize this, we can quit sketch our parabola. So we see that the vertex is in the third quadrant and our parabola again opens upwards and now we can see that our minimum value is at the vertex and for the y coordinate it goes from negative six to positive infinity. And so now we can see that our range encompasses all real numbers at or above negative six. And so with this we can write our range in interval notation as -6, which is included. So enclosed by a bracket to positive infinity in that four hour domain it just follows any other quadratic function and goes from negative infinity to positive infinity. And therefore we are left with answer choice D with a domain from negative infinity to positive infinity. And I range from negative in negative six included to positive infinity. Thanks for watching. I hope you found this video helpful and I'll see you again next time

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In Exercises 45–48, give the domain and the range of each quadratic function whose graph is described. The vertex is and the parabola opens up.