Final answer:
To determine the width of the dish, the quadratic equation y=275x^2-43x-323 is solved for x when y=0. This can be done graphically by finding the x-intercepts of the parabola, which represent the extremes of the dish's width.
Step-by-step explanation:
To find the width of the dish represented by the parabola y=275x2−43x∓323 when y=0, we need to solve the quadratic equation for the values of x that make y equal to zero. This gives us the x-coordinates of the points where the parabola intersects the x-axis, which in the context of the radio telescope dish, would represent the points at the edge of the dish on either side of the center.
We can solve the equation by factoring, completing the square, or using the quadratic formula. However, since we are asked to solve by graphing, we would graph the quadratic equation and look for the points where the curve crosses the x-axis. These points are referred to as the x-intercepts or zeros of the function. The distance between these two points, measured along the x-axis, will give us the width of the dish.
To solve by graphing, plot a graph with the given equation, or use a graphing calculator or software. The points where the parabola intersects the x-axis (where y=0) represent the width of the dish at the top.