At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
[tex]y = x^2 + 8x + 10\\\\The\ vertex=(p;\ q)\ \ \ and\ \ \ p=- \frac{b}{2a} ;\ \ \ q=- \frac{\Delta}{4a} ;\ \ \ \Delta=b^2-4ac\\\\\Delta=8^2-4\cdot1\cdot10=64-40=24\\\\p=- \frac{8}{2\cdot1} =-4\\\\q=- \frac{24}{4\cdot1} =-6\\\\the\ vertex=(-4;-6)[/tex]
[tex]y = x^2 + 8x + 10 \\ \\the \ standard \ form \ y = ax^2 + bx + c \\\\of \ a \ function \ into \ vertex \ form \ y = a(x - h)^2 + k ,\\ \\ we \ have \ to \ write \ the \ equation \ in \ the \ complete \ square \ form \\\\\ and \ vertex(h, k) \ is \ given \ by:[/tex]
[tex]h = \frac{-b}{2a} , \ \ k = c -\frac{b^2}{4a } \\ \\y = a(x - h)^2+k[/tex]
opens up for a > 0
[tex] a=1 , \ \ b=8, \ \ c=10 \\ \\h= \frac{-8}{2}=-4[/tex]
[tex]k= 10-\frac{8^2}{4}=10-\frac{64}{4}=10-16=-6 \\ \\y=(x-(-4))^2+(-6)\\ \\y=(x+4)^2-6[/tex]
[tex]h = \frac{-b}{2a} , \ \ k = c -\frac{b^2}{4a } \\ \\y = a(x - h)^2+k[/tex]
opens up for a > 0
[tex] a=1 , \ \ b=8, \ \ c=10 \\ \\h= \frac{-8}{2}=-4[/tex]
[tex]k= 10-\frac{8^2}{4}=10-\frac{64}{4}=10-16=-6 \\ \\y=(x-(-4))^2+(-6)\\ \\y=(x+4)^2-6[/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.