Determine the Positive and Negative Domains of y = 2x² - 5x + 3

Great question! The positive domain means where the function value $y > 0$, not where $x > 0$. For this function, y is positive when $x < 1$ or $x > 1.5$, regardless of whether x itself is positive or negative.

First, find the zeros by setting the function equal to zero. These zeros divide the number line into intervals. Then test a value from each interval to see if the function is positive or negative there.

Because this parabola opens upward (coefficient of $x^2$ is positive), it's positive on the outside of the zeros and negative between them. The function crosses the x-axis at each zero, changing sign.

Use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$. For $2x^2-5x+3$, this gives $x = \frac{5 \pm 1}{4}$, so x = 1 and x = 1.5.

Use parentheses for intervals that don't include endpoints. The positive domain is $(-\infty, 1) \cup (1.5, \infty)$ and the negative domain is $(1, 1.5)$.