Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

write a quadratic function that fits points (0,3), (-1,-2), (-2,-5)

Sagot :

naǫ
[tex]y=ax^2+bx+c \\ \\ (0,3) \\ 3=a \times 0^2+b \times 0 + c \\ 3=c \\ \\ \hbox{so the equation is:} \\ y=ax^2+bx+3 \\ \\ (-1,-2) \\ -2=a \times (-1)^2+b \times (-1) + 3 \\ -2=a-b+3 \\ -2-3=a-b \\ -5=a-b[/tex]

[tex](-2,-5) \\ -5=a \times (-2)^2+b \times (-2) + 3 \\ -5=4a-2b+3 \\ -5-3=4a-2b \\ -8=4a-2b \\ \\ \hbox{solve the system of equations:} \\ -5=a-b \ \ \ |\times (-2) \\ -8=4a-2b \\ \\ 10=-2a+2b \\ \underline{-8=4a-2b \ \ } \\ 10-8=4a-2a \\ 2=2a \\ \frac{2}{2}=a \\ a=1 \\ \\ -5=a-b \\ -5=1-b \\ -5-1=-b \\ -6=-b \\ b=6 \\ \\ \boxed{y=x^2+6x+3}[/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.