Solve y=-5x²-10: Finding Where Function is Positive

To solve this problem, we need to analyze the quadratic function given by:

1. Step 1: Find the vertex of the parabola.
The formula for a quadratic function is $y = ax^2 + bx + c$. For our function, $a = -5$, $b = 0$, $c = -10$.
Since $b = 0$, the x-coordinate of the vertex is $x = 0$.

2. Step 2: Calculate the y-coordinate of the vertex.
Substitute $x = 0$ into the function:
$y = -5(0)^2 - 10 = -10$.

3. Step 3: Analyze the parabola.
The vertex is at (0, -10). Since the vertex itself is below the x-axis and the parabola opens downwards (given by a < 0 ), the entire parabola is below the x-axis.

As a result, there are no values of $x$ for which the function $y = -5x^2 - 10$ is greater than 0.

Therefore, the correct answer to the problem is that there are no values of $x$.