Sketch a cubic function (third degree polynomial function) y = p(x) with two distinct zeros at x= 1 x= 4 and a local maximum at x= 4. Then determine a formula for your function. [Hint: you will have one double root.

Sketch :

Formula

Problem 3 (3 points): Find the formula for the quadratic function whose graph has a vertex of (1, 2) and passes through the point (-1, -6).

Step 1: Use the coordinates of the vertex to write p(x) in the form: p(x)=a(x-h)^2 +k, where a is not known.

Step 2: Use the coordinates of the second point to solve for the leading coefficient, .

Put steps 1 and 2 together and determne p(x)