1. Which of the following is a quadratic function? $$ \begin{array}{ll} ext { (1) } y=3 x-2 & ext { (3) } y=x^{2}-4 \ ext { (2) } y=x^{3}+2 x^{2}-1 & ext { (4) } y=6(2)^{x}\end{array} $$

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1. Which of the following is a quadratic function? $$ \begin{array}{ll}	ext { (1) } y=3 x-2 & 	ext { (3) } y=x^{2}-4 \ 	ext { (2) } y=x^{3}+2 x^{2}-1 & 	ext { (4) } y=6(2)^{x}\end{array} $$

UpStudy AI · Accepted Answer

To determine which of the given functions is a quadratic function, we need to identify the characteristics of a quadratic function. A quadratic function is typically in the form:

$$
y = ax^2 + bx + c
$$

where $$a$$, $$b$$, and $$c$$ are constants, and $$a \neq 0$$.

Now, let's analyze each of the provided options:

1. **Option (1)**: $$y = 3x - 2$$
   - This is a linear function (not quadratic) because it can be expressed in the form $$y = mx + b$$.

2. **Option (2)**: $$y = x^3 + 2x^2 - 1$$
   - This is a cubic function (not quadratic) because the highest power of $$x$$ is 3.

3. **Option (3)**: $$y = x^2 - 4$$
   - This is a quadratic function because it is in the form $$y = ax^2 + bx + c$$ with $$a = 1$$, $$b = 0$$, and $$c = -4$$.

4. **Option (4)**: $$y = 6(2)^x$$
   - This is an exponential function (not quadratic) because it involves $$2^x$$, which is not a polynomial.

Based on this analysis, the only quadratic function among the options is:

**Option (3)**: $$y = x^2 - 4$$.
Option (3) $$ y = x^2 - 4 $$ is a quadratic function.

1. Which of the following is a quadratic function? \( \begin{array}{ll}\text { (1) } y=3 x-2 & \text { (3) } y=x^{2}-4 \\ \text { (2) } y=x^{3}+2 x^{2}-1 & \text { (4) } y=6(2)^{x}\end{array} \)

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