1. The problem asks to determine if each given function is quadratic (QF) or not quadratic (NFQ). 2. A quadratic function is a polynomial function of degree 2, which means the highest power of $x$ is 2. 3. Let's analyze each function: a. $f(x) = \sqrt{8} + 2x^2 - 3x$ - $\sqrt{8}$ is a constant. - The highest power of $x$ is 2 (from $2x^2$). - So, this is a quadratic function (QF). b. $f(x) = 9x^2 - 3x + \frac{1}{2}$ - Highest power of $x$ is 2. - This is a quadratic function (QF). c. $f(x) = 2x^2 + 2x - 9$ - Highest power of $x$ is 2. - This is a quadratic function (QF). d. $f(x) = 3x - 1 + 5x^2 + 3$ - Rearranged: $5x^2 + 3x + (3 - 1) = 5x^2 + 3x + 2$ - Highest power of $x$ is 2. - This is a quadratic function (QF). e. $f(x) = (6x^2 - 2)^2$ - Expanding: $$ (6x^2 - 2)^2 = (6x^2)^2 - 2 \times 6x^2 \times 2 + (-2)^2 = 36x^4 - 24x^2 + 4 $$ - The highest power of $x$ is 4. - This is NOT a quadratic function (NFQ). Final answers: a. QF b. QF c. QF d. QF e. NFQ