The given equation \( y = -10x^2 + 20x + 80 \) is a quadratic equation in standard form \( y = ax^2 + bx + c \), where \( a = -10 \), \( b = 20 \), and \( c = 80 \).
To determine the shape of the graph, we look at the coefficient of \( x^2 \) (which is \( a \)):
- If \( a > 0 \), the parabola opens upwards (U-shaped).
- If \( a < 0 \), the parabola opens downwards (n-shaped).
Since \( a = -10 \) (which is less than 0), the associated graph of the equation is a downward-opening parabola.
The solutions \( x = -2 \) and \( x = 4 \) represent the x-intercepts of the parabola, meaning those are the points where the graph intersects the x-axis.
In summary, the general shape of the associated graph is a downward-opening parabola (inverted U-shape).
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