Y=-4x квадрат

The equation you've provided is a quadratic function in the form of \( y = -4x^2 \). This is a parabola that opens downwards because the coefficient of \( x^2 \) is negative. Here are some important characteristics of the parabola represented by this equation: 1. **Vertex**: The vertex of the parabola is at the origin (0, 0), since there are no additional linear or constant terms in the equation. 2. **Axis of Symmetry**: The axis of symmetry is the vertical line \( x = 0 \). 3. **Direction**: The parabola opens downward due to the negative coefficient (-4). 4. **Intercepts**: - **Y-intercept**: When \( x = 0 \), \( y = -4(0)^2 = 0 \). So, the y-intercept is at the point (0, 0). - **X-intercepts**: To find the x-intercepts, set \( y = 0 \): \[ 0 = -4x^2 \] This gives \( x = 0 \) as the only x-intercept. 5. **Shape**: The coefficient \(-4\) indicates that the parabola is relatively narrow; it opens downward and is steeper compared to a parabola like \( y = -x^2 \). If you need further analysis or specific details, such as graphing the function or finding its maximum value, feel free to ask!