Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Answer:
Step-by-step explanation:
Given: f(1)= f(3) = 0
Putting f(1) = a(1)^2 + b(1) + c
= a + b + c
Putting f(3) = a(3)^2 + b(3) + c
= 9a + 3b + c
Putting f(0)=a(0)^2 + b(0) + c = -3
= c = -3
putting c = -3 In equation (1) and equation (2) we get,
a + b - 3 = 0 9a + 3b - 3 = 0
a + b = 3 3(3a+b) = 3
a = 3 - b 3a + b = 1
3(3-b) + b = 1 [Putting a = 3 - b ]
9 - 3b +b = 1
-2b = -8
b = 4
Answer:
b = 4
Step-by-step explanation:
To find the value of b in the quadratic function f(x) = ax² + bx + c, begin by substituting f(0) = -3, and solve for c:
[tex]f(0) = -3\\\\a(0)^2+b(0)+c=-3\\\\0+0+c=-3\\\\c=-3[/tex]
Substitute c = -3 into the function:
[tex]f(x) = ax^2+bx-3[/tex]
Now, substitute f(1) = 0 and f(3) = 0 into the function to form a system of equations:
[tex]f(1)=0\\\\a(1)^2+b(1)-3=0\\\\a+b-3=0[/tex]
[tex]f(3)=0\\\\a(3)^2+b(3)-3=0\\\\9a+3b-3=0[/tex]
So, the system of equations is:
[tex]\begin{cases}a+b-3=0\\9a+3b-3=0\end{cases}[/tex]
Rearrange the first equation to isolate a:
[tex]a+b-3=0\\\\a=3-b[/tex]
Substitute a = 3 - b into the second equation and solve for b:
[tex]9(3-b)+3b-3=0\\\\27-9b+3b-3=0\\\\24-6b=0\\\\6b=24\\\\b=4[/tex]
Therefore, the value of b is:
[tex]\Large\boxed{\boxed{b=4}}[/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
