Fill in the blank(s) to correctly complete each sentence. The vertex of the graph of ƒ(x) = x^2 + 2x + 4 has x-coordinate ____ .

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Hey, everyone in this problem, we're asked to choose the correct option to fill in the blank. The Y coordinate of the vertex of the graph Y equals X squared minus 24 X plus 149 is we're given four answer choices. Option A K is equal to 12. Option B K is equal to five. Option C K is equal to negative five and option D K is equal to negative 12. Now, we're gonna start by writing the equation we were given, we have Y is equal to X squared minus X plus 149. We want to put this into vertex form so that we can pick out that Y coordinate of the vertex we're interested in. Now recall that vertex form is Y is equal to a multiplied by X minus H squared plus K and the coordinates of the vertex are given by H comma K. Now the Y coordinate is gonna be that K value. And so that is what we're interested in finding that K value or that Y coordinate. So we wanna write our equation in this vertex form so that we can find K. Now, in order to do that, we want to complete the square with the first two terms, we have X squared minus 24 X. We want to complete that square. Now, we can write this as X squared minus X plus 144. We initially had plus 149. So we can write this as plus 144 plus five. OK. These two equations are equivalent, we've just broken that constant into two parts. Now, the first three terms X squared minus 24 X plus 144 represent a perfect square, X minus 12. OK. So we can write these as X minus 12 squared and then we're left with plus five at the end and you can check your work, you can go backwards, OK? We have X minus 12 all squared, you can expand this and you'll see that you get X squared minus 24 X plus 144. So that's a nice thing about completing the square or changing this into vertex form. You can always go back and double check um that your work is correct. So now this is in vertex form, we have Y is equal to A which is one multiplied by X minus H which is 12 all squared plus K, which is five. OK. And so the K value we are interested in is equal to five. And that represents the y coordinate of our vertex. And so we have K equals five which corresponds with answer choice. B thanks everyone for watching. I hope this video helped see you in the next one.

Fill in the blank(s) to correctly complete each sentence. The vertex of the graph of ƒ(x) = x^2 + 2x + 4 has x-coordinate ____ .

Verified Solution

Key Concepts

Vertex of a Quadratic Function

Standard Form of a Quadratic Function

Completing the Square