Solve (x-4.4)(x-2.3) < 0: Finding Negative Function Values

To determine when the quadratic function $y = (x - 4.4)(x - 2.3)$ is negative, we need to analyze the sign of the product across the different intervals defined by its roots.

• Step 1: Identify the roots of the function. The roots occur when each factor equals zero, which are $x = 2.3$ and $x = 4.4$.
• Step 2: Divide the x-axis into intervals based on these roots: $x < 2.3$, $2.3 < x < 4.4$, and $x > 4.4$.
• Step 3: Test a value from each interval:
  • For $x < 2.3$, try $x = 2$: $y = (2 - 4.4)(2 - 2.3) = (-2.4)(-0.3) = 0.72$, so the product is positive.
  • For $2.3 < x < 4.4$, try $x = 3$: $y = (3 - 4.4)(3 - 2.3) = (-1.4)(0.7) = -0.98$, so the product is negative.
  • For $x > 4.4$, try $x = 5$: $y = (5 - 4.4)(5 - 2.3) = (0.6)(2.7) = 1.62$, so the product is positive.

From this analysis, we see that the quadratic function is negative for values of $x$ in the interval $2.3 < x < 4.4$. This is the range where the function changes sign from positive to negative back to positive.

Therefore, the correct answer is $2.3 < x < 4.4$.