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The solutions of the quadratic equation find the values of y (the value of the function f(x)) that are zero. This can be seen on the graph. The value of x at which the function crosses the x axis are the x values where the function equals zero. All points on the x axis have a y value of 0.
A real life example could be throwing a ball through the air at an angle. The path of the ball follows a parabola (the shape of a quadratic function). The solutions to the quadratic equation will show the times when the ball is at the position 0 also known as the ground.
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