Answer:
A, D
Explanation:
You want to identify the quadratic functions among the equations listed.
Quadratic
A quadratic function is a relation whose output value is related to the square of the input value. When expressed as a polynomial equation, the polynomial will have terms of degree 2 or less.
A. y = 2x²
This is a quadratic function.
B. 3 = 2x² -8
This is not a function. It describes two values of input x, but no corresponding values of output. (x = ±√5.5)
Even if 3 is considered an output value, we cannot say it depends on the square of x. It is simply constant.
C. y = -2 +2x -8
The polynomial relating x to y is of degree 1. This is not a quadratic function.
D. y +3x = 2x² -8
The relation between x and y is quadratic. The relation describes y as a quadratic function of x. (The functional relation might be written more conventionally as y = 2x² -3x -8.)
E. y +3x² = 2x +3x² -8
The relation between x and y is linear. The two 2nd-degree terms cancel each other and do not contribute to the relation. This is not a quadratic function.
Choices A and D show quadratic functions.
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Additional comment
A function is usually an equation that can be written in the form ...
f(x) = (some expression involving x)
It tells the output (f(x)) for each input (x). The relation can be described by ordered pairs (x, f(x)).
The "expression involving x" may just be a constant, not involving x at all. That is, the relation ...
f(x) = 3
is still considered to be a function. Every input has an output of 3 in this case.
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