Answer :
To determine which of the given points lies on the graph of the function [tex]\( f(x) = 2x^2 - 4 \)[/tex], we need to plug each [tex]\( x \)[/tex]-value from the options into the function and see if the resulting [tex]\( f(x) \)[/tex]-value matches the provided [tex]\( y \)[/tex]-value.
Let's evaluate [tex]\( f(x) \)[/tex] for each option:
Option A: [tex]\( f(3) \)[/tex]
[tex]\[ f(3) = 2(3)^2 - 4 = 2 \cdot 9 - 4 = 18 - 4 = 14 \][/tex]
The result is [tex]\( f(3) = 14 \)[/tex], not [tex]\( 16 \)[/tex]. This option is incorrect.
Option B: [tex]\( f(-5) \)[/tex]
[tex]\[ f(-5) = 2(-5)^2 - 4 = 2 \cdot 25 - 4 = 50 - 4 = 46 \][/tex]
The result matches provided [tex]\( f(-5) = 46 \)[/tex]. This option is correct.
Option C: [tex]\( f(4) \)[/tex]
[tex]\[ f(4) = 2(4)^2 - 4 = 2 \cdot 16 - 4 = 32 - 4 = 28 \][/tex]
The result matches provided [tex]\( f(4) = 28 \)[/tex]. This option is correct.
Option D: [tex]\( f(-2) \)[/tex]
[tex]\[ f(-2) = 2(-2)^2 - 4 = 2 \cdot 4 - 4 = 8 - 4 = 4 \][/tex]
The result is [tex]\( f(-2) = 4 \)[/tex], not [tex]\( -8 \)[/tex]. This option is incorrect.
After evaluating each option, we can conclude that the points that lie on the graph of the function [tex]\( f(x) = 2x^2 - 4 \)[/tex] are:
- Option B: [tex]\( f(-5) = 46 \)[/tex]
- Option C: [tex]\( f(4) = 28 \)[/tex]
Thus, the correct points on the graph of the function are those found in Option B and Option C.
Let's evaluate [tex]\( f(x) \)[/tex] for each option:
Option A: [tex]\( f(3) \)[/tex]
[tex]\[ f(3) = 2(3)^2 - 4 = 2 \cdot 9 - 4 = 18 - 4 = 14 \][/tex]
The result is [tex]\( f(3) = 14 \)[/tex], not [tex]\( 16 \)[/tex]. This option is incorrect.
Option B: [tex]\( f(-5) \)[/tex]
[tex]\[ f(-5) = 2(-5)^2 - 4 = 2 \cdot 25 - 4 = 50 - 4 = 46 \][/tex]
The result matches provided [tex]\( f(-5) = 46 \)[/tex]. This option is correct.
Option C: [tex]\( f(4) \)[/tex]
[tex]\[ f(4) = 2(4)^2 - 4 = 2 \cdot 16 - 4 = 32 - 4 = 28 \][/tex]
The result matches provided [tex]\( f(4) = 28 \)[/tex]. This option is correct.
Option D: [tex]\( f(-2) \)[/tex]
[tex]\[ f(-2) = 2(-2)^2 - 4 = 2 \cdot 4 - 4 = 8 - 4 = 4 \][/tex]
The result is [tex]\( f(-2) = 4 \)[/tex], not [tex]\( -8 \)[/tex]. This option is incorrect.
After evaluating each option, we can conclude that the points that lie on the graph of the function [tex]\( f(x) = 2x^2 - 4 \)[/tex] are:
- Option B: [tex]\( f(-5) = 46 \)[/tex]
- Option C: [tex]\( f(4) = 28 \)[/tex]
Thus, the correct points on the graph of the function are those found in Option B and Option C.