Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To find the value of [tex]\( a \)[/tex] in the quadratic function, we start by recalling the general form of a quadratic equation:
[tex]\[ y = ax^2 + bx + c \][/tex]
Given the table of values, we have six points: [tex]\((0, -3)\)[/tex], [tex]\((1, -3.75)\)[/tex], [tex]\((2, -4)\)[/tex], [tex]\((3, -3.75)\)[/tex], [tex]\((4, -3)\)[/tex], and [tex]\((5, -1.75)\)[/tex].
We can use three of these points to set up a system of equations to solve for [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex].
First, we use the point [tex]\((0, -3)\)[/tex]:
[tex]\[ -3 = a(0)^2 + b(0) + c \][/tex]
This simplifies to:
[tex]\[ c = -3 \][/tex]
Next, we use the point [tex]\((1, -3.75)\)[/tex]:
[tex]\[ -3.75 = a(1)^2 + b(1) - 3 \][/tex]
[tex]\[ -3.75 = a + b - 3 \][/tex]
[tex]\[ a + b = -0.75 \][/tex]
Then, we use the point [tex]\((2, -4)\)[/tex]:
[tex]\[ -4 = a(2)^2 + b(2) - 3 \][/tex]
[tex]\[ -4 = 4a + 2b - 3 \][/tex]
[tex]\[ 4a + 2b = -1 \][/tex]
We now have the system of equations:
1. [tex]\( c = -3 \)[/tex]
2. [tex]\( a + b = -0.75 \)[/tex]
3. [tex]\( 4a + 2b = -1 \)[/tex]
Since [tex]\( c \)[/tex] has already been determined to be [tex]\(-3\)[/tex], we solve for [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
We can simplify the third equation:
[tex]\[ 4a + 2b = -1 \][/tex]
[tex]\[ 2a + b = -0.5 \][/tex]
We have two equations now:
1. [tex]\( a + b = -0.75 \)[/tex]
2. [tex]\( 2a + b = -0.5 \)[/tex]
Subtract the first equation from the second:
[tex]\[ (2a + b) - (a + b) = -0.5 - (-0.75) \][/tex]
[tex]\[ 2a + b - a - b = -0.5 + 0.75 \][/tex]
[tex]\[ a = 0.25 \][/tex]
Thus, the value of [tex]\( a \)[/tex] is [tex]\( 0.25 \)[/tex].
Therefore, the correct answer is:
D. [tex]\(\frac{1}{4}\)[/tex]
[tex]\[ y = ax^2 + bx + c \][/tex]
Given the table of values, we have six points: [tex]\((0, -3)\)[/tex], [tex]\((1, -3.75)\)[/tex], [tex]\((2, -4)\)[/tex], [tex]\((3, -3.75)\)[/tex], [tex]\((4, -3)\)[/tex], and [tex]\((5, -1.75)\)[/tex].
We can use three of these points to set up a system of equations to solve for [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex].
First, we use the point [tex]\((0, -3)\)[/tex]:
[tex]\[ -3 = a(0)^2 + b(0) + c \][/tex]
This simplifies to:
[tex]\[ c = -3 \][/tex]
Next, we use the point [tex]\((1, -3.75)\)[/tex]:
[tex]\[ -3.75 = a(1)^2 + b(1) - 3 \][/tex]
[tex]\[ -3.75 = a + b - 3 \][/tex]
[tex]\[ a + b = -0.75 \][/tex]
Then, we use the point [tex]\((2, -4)\)[/tex]:
[tex]\[ -4 = a(2)^2 + b(2) - 3 \][/tex]
[tex]\[ -4 = 4a + 2b - 3 \][/tex]
[tex]\[ 4a + 2b = -1 \][/tex]
We now have the system of equations:
1. [tex]\( c = -3 \)[/tex]
2. [tex]\( a + b = -0.75 \)[/tex]
3. [tex]\( 4a + 2b = -1 \)[/tex]
Since [tex]\( c \)[/tex] has already been determined to be [tex]\(-3\)[/tex], we solve for [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
We can simplify the third equation:
[tex]\[ 4a + 2b = -1 \][/tex]
[tex]\[ 2a + b = -0.5 \][/tex]
We have two equations now:
1. [tex]\( a + b = -0.75 \)[/tex]
2. [tex]\( 2a + b = -0.5 \)[/tex]
Subtract the first equation from the second:
[tex]\[ (2a + b) - (a + b) = -0.5 - (-0.75) \][/tex]
[tex]\[ 2a + b - a - b = -0.5 + 0.75 \][/tex]
[tex]\[ a = 0.25 \][/tex]
Thus, the value of [tex]\( a \)[/tex] is [tex]\( 0.25 \)[/tex].
Therefore, the correct answer is:
D. [tex]\(\frac{1}{4}\)[/tex]
B as the tabular ends after going through a negative current stream.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
