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Which equation represents a quadratic function with a leading coefficient of 2 and a constant term of -3?

A. [tex]f(x)=2x^3 - 3[/tex]
B. [tex]f(x)=-3x^2 - 3x + 2[/tex]
C. [tex]f(x)=-3x^3 + 2[/tex]
D. [tex]f(x)=2x^2 + 3x - 3[/tex]

Sagot :

GinnyAnsweridn
To determine which equation represents a quadratic function with a leading coefficient of 2 and a constant term of -3, let's analyze each option step by step.

1. [tex]\( f(x) = 2x^3 - 3 \)[/tex]
This is a cubic function because the highest power of [tex]\( x \)[/tex] is 3. We need a quadratic function, so this is not the correct choice.

2. [tex]\( f(x) = -3x^2 - 3x + 2 \)[/tex]
This is a quadratic function because the highest power of [tex]\( x \)[/tex] is 2. However, the leading coefficient (coefficient of [tex]\( x^2 \)[/tex]) is -3, not 2. Thus, this is not the correct choice.

3. [tex]\( f(x) = -3x^3 + 2 \)[/tex]
This is a cubic function because the highest power of [tex]\( x \)[/tex] is 3. We need a quadratic function, so this is not the correct choice.

4. [tex]\( f(x) = 2x^2 + 3x - 3 \)[/tex]
This is a quadratic function because the highest power of [tex]\( x \)[/tex] is 2. The leading coefficient (coefficient of [tex]\( x^2 \)[/tex]) is 2, and the constant term is -3. This matches the given requirements perfectly.

Therefore, the equation that represents a quadratic function with a leading coefficient of 2 and a constant term of -3 is:
[tex]\[ \boxed{f(x) = 2x^2 + 3x - 3} \][/tex]
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