(a) Find a quadratic function whose x-intercepts are -5 and 3 with a = 1; a = 2; a = -2; a = 5.

(b) How does the value of a affect the intercepts?

(c) How does the value of a affect the axis of symmetry?

(d) How does the value of a affect the vertex?

(e) Compare the x-coordinate of the vertex with the midpoint of the x-intercepts. What might you conclude?

Answer problem using above: A quadratic function of the form f(x) = ax² + bx + c with b² - 4ac > 0 may also be written in the form f (x) = a(x – r₁)(x - r₂), where r₁ and r₂ are the x-intercepts of the graph of the quadratic function.