Solve the Quadratic Function -2x² - 8x - 10: Find x When f(x) > 0

Look at the following function:

$y=-2x^2-8x-10$

Determine for which values of $x$ the following is true:

$f\left(x\right)>0$

To solve for where $y = -2x^2 - 8x - 10 > 0$, we must analyze the quadratic equation.

First, identify the coefficients: $a = -2$, $b = -8$, and $c = -10$.
The parabola opens downwards since $a < 0$.

Calculate the discriminant $\Delta = b^2 - 4ac = (-8)^2 - 4(-2)(-10) = 64 - 80 = -16$.
Since the discriminant is negative, there are no real roots.

As a result, the quadratic does not intersect the x-axis, meaning it has no intervals where it is positive.
Because the parabola opens downward and lies entirely below the x-axis, the function $y = -2x^2 - 8x - 10$ has no positive domain.

Thus, the function $f(x) = -2x^2 - 8x - 10$ is never greater than zero.

Therefore, the solution to the problem is The function has no positive domain.