Using the graph of the function y = -x² + 2x + 3, find the values of x at which the value of the function is 3.

It is necessary to build graphs of the functions y = – x ^ 2 + 2x + 3 and y = 3. The abscissas of the intersection points of the graphs will be solutions.

1) y = 3 – a straight line parallel to the ox axis and passing through the point (0; 3), in the drawing it is a blue straight line.

2) y = – x ^ 2 + 2x + 3 is a quadratic function, the graph is a parabola, the branches of which look down (since the coefficient a <0); find the abscissa of the vertex of the parabola by the formula n = – b / (2a);

n = – 2 / (2 * (- 1)) = – 2 / (- 2) = 1 – build a table of values, taking into account that the graph is symmetric with respect to the straight line passing through the vertex of the parabola, parallel to oy;

according to the table, we will build a graph in the same coordinate system as the straight line (green parabola);

The graphs intersect at two points (0; 3) and (2; 3); the abscissas of these points are the solution.

Answer. x = 0; x = 2.