Use the table of values that represent points on the graph of a quadratic function. By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function. y X X y -2 1 -1 0 0 1 1 9 Use the table to determine the turning point (vertex) of the graph of the quadratic function. Recall that the standard form of a quadratic function is f(x) = a(x - h)2 + k where (h, k) represents the vertex. How can the vertex and another point on the graph be used to solve for the stretch factor a? What algebraic manipulation will help to write the equation of the quadratic function in general form f(x) = ax2 + bx + c? 4 2

a) Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.) Vertex:  (−2, −11);   point:  (0, −3)   b) Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.) Vertex: (−7, −2);   point:  (−8, 0)

Identify the vertex, axis of symmetry, and x-intercept(s).  vertex     (x, f(x)) =               axis of symmetry               x-intercept     (x, f(x)) =