Answer:
[tex]\displaystyle y = [x - 3]^2 + 6[/tex]
Step-by-step explanation:
Use the method called complete the square, but in this case, we need to take half of the B-term and square the result afterward. Here is how it is done:
[tex]\displaystyle [\frac{b}{2}]^2 \hookrightarrow [\frac{-6}{2}]^2; 9 \\ \\ \boxed{[x - 3]^2} \hookrightarrow x^2 - 6x + 9[/tex]
Now, after you get an equation from using this method, you must follow ONE MORE PROCEDURE, which is figuring the quantity out that when added to 9, you get 15, and that will be 6. So, with that, you have your vertex equation:
[tex]\displaystyle y = A[x - h]^2 + k \\ \\ \boxed{\boxed{y = [x - 3]^2 + 6}}[/tex]
**In the event you have a quadratic equation, if you are asked to locate the vertex, IF factourable, convert the quadratic equation to a vertex equation, where [tex]\displaystyle [h, k][/tex]represents the vertex:
[tex]\displaystyle y = Ax^2 + Bx + C \hookrightarrow y = A[x - h]^2 + k[/tex]
I am delighted to assist you at any time.
