Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To determine which function has the greater maximum value, we need to analyze the given function [tex]\( f(x) = -2x^2 + 4x + 3 \)[/tex] and compare it to the function [tex]\( g(x) \)[/tex] presented in the graph (though we do not have the actual graph provided).
Let's start by finding the maximum value of [tex]\( f(x) \)[/tex]:
1. Identify the quadratic function form:
The function [tex]\( f(x) = -2x^2 + 4x + 3 \)[/tex] is in the standard form [tex]\( ax^2 + bx + c \)[/tex], where [tex]\( a = -2 \)[/tex], [tex]\( b = 4 \)[/tex], and [tex]\( c = 3 \)[/tex].
2. Vertex formula for quadratic functions:
The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] is given by the x-coordinate at [tex]\( x = -\frac{b}{2a} \)[/tex].
3. Calculate the x-coordinate of the vertex:
[tex]\[ x = -\frac{b}{2a} = -\frac{4}{2 \times -2} = \frac{4}{4} = 1 \][/tex]
4. Find the maximum value by plugging the x-coordinate into [tex]\( f(x) \)[/tex]:
[tex]\[ f(1) = -2(1)^2 + 4(1) + 3 \][/tex]
Simplifying the equation:
[tex]\[ f(1) = -2(1) + 4 + 3 = -2 + 4 + 3 = 5 \][/tex]
We have now found that the maximum value of [tex]\( f(x) \)[/tex] is 5.
Next, without having the graph of [tex]\( g(x) \)[/tex] and its maximum value explicitly given, we need to make our conclusion based on the information about [tex]\( f(x) \)[/tex]:
- If the maximum value from the graph of [tex]\( g(x) \)[/tex] is higher than 5, then [tex]\( g(x) \)[/tex] has a greater maximum value.
- If the maximum value from the graph of [tex]\( g(x) \)[/tex] is lower than 5, then [tex]\( f(x) \)[/tex] has a greater maximum value.
- If the maximum value from the graph of [tex]\( g(x) \)[/tex] is exactly 5, then both functions have the same maximum value.
Given that we only know the maximum value of [tex]\( f(x) \)[/tex] is 5 from our calculation, and without further information on [tex]\( g(x) \)[/tex], we are unable to make a definitive comparison.
Thus, based on the information about the maximum value of [tex]\( f(x) \)[/tex], we must assume that to determine which function has the greater maximum value, we must refer to the graph of [tex]\( g(x) \)[/tex].
Let's start by finding the maximum value of [tex]\( f(x) \)[/tex]:
1. Identify the quadratic function form:
The function [tex]\( f(x) = -2x^2 + 4x + 3 \)[/tex] is in the standard form [tex]\( ax^2 + bx + c \)[/tex], where [tex]\( a = -2 \)[/tex], [tex]\( b = 4 \)[/tex], and [tex]\( c = 3 \)[/tex].
2. Vertex formula for quadratic functions:
The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] is given by the x-coordinate at [tex]\( x = -\frac{b}{2a} \)[/tex].
3. Calculate the x-coordinate of the vertex:
[tex]\[ x = -\frac{b}{2a} = -\frac{4}{2 \times -2} = \frac{4}{4} = 1 \][/tex]
4. Find the maximum value by plugging the x-coordinate into [tex]\( f(x) \)[/tex]:
[tex]\[ f(1) = -2(1)^2 + 4(1) + 3 \][/tex]
Simplifying the equation:
[tex]\[ f(1) = -2(1) + 4 + 3 = -2 + 4 + 3 = 5 \][/tex]
We have now found that the maximum value of [tex]\( f(x) \)[/tex] is 5.
Next, without having the graph of [tex]\( g(x) \)[/tex] and its maximum value explicitly given, we need to make our conclusion based on the information about [tex]\( f(x) \)[/tex]:
- If the maximum value from the graph of [tex]\( g(x) \)[/tex] is higher than 5, then [tex]\( g(x) \)[/tex] has a greater maximum value.
- If the maximum value from the graph of [tex]\( g(x) \)[/tex] is lower than 5, then [tex]\( f(x) \)[/tex] has a greater maximum value.
- If the maximum value from the graph of [tex]\( g(x) \)[/tex] is exactly 5, then both functions have the same maximum value.
Given that we only know the maximum value of [tex]\( f(x) \)[/tex] is 5 from our calculation, and without further information on [tex]\( g(x) \)[/tex], we are unable to make a definitive comparison.
Thus, based on the information about the maximum value of [tex]\( f(x) \)[/tex], we must assume that to determine which function has the greater maximum value, we must refer to the graph of [tex]\( g(x) \)[/tex].
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
