Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
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]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
