A quadratic graph is a type of parabolic graph that can be represented by the equation y = ax^2 + bx + c, where a, b, and c are constants and x is the variable. The graph of this equation is a parabola that opens either up or down, depending on the value of a.
The equation y = x^2 + 2x - 3 is an example of a quadratic graph. It can be written in the standard form of a quadratic equation as y = x^2 + 2x - 3, where a = 1, b = 2 and c = -3.
The x^2 term in the equation is known as the quadratic term, and it is responsible for the parabolic shape of the graph. The x term and the constant term, 2x and -3, respectively, determine the location of the vertex and the direction of the parabola.
The vertex of the parabola is the point where the parabola changes direction. It can be found by using the formula x = -b/2a, which in this case is x = -2/2 = -1 and y = f(-1) = -1.
The graph of y = x^2 + 2x - 3 is a parabola that opens upwards and the vertex of the parabola is (-1,-1)
In summary, a quadratic graph is a parabolic graph represented by the equation y = ax^2 + bx + c, where a, b, and c are constants. The x^2 term gives the parabolic shape to the graph, the x term and the constant term determine the vertex and the direction of the parabola respectively.