1. Write the equation of the constant function, if possible, which passes throught the point P(4,5).

2. Write the equation of the cubic function, if possible, which passes through the points A(0,1), B(2,9), C(4,12), and D(10,15). Express all coefficients as fractions.

3. Determine the coordinates of the vertex of the parabola

y= -1/4 (x+2)^2 -3

4. Determine the coordinates of the vertex of the parabola

y= 3x^2 -6x +1

5. Determine the coordinates of the point of symmetry for the cubic equation

y= 4x^3 - 6x^2 + 9x -3

6. Write the equation of the quadratic function which has x-intercepts 2, and -1, and a y-intercept of 6.

7. Factor completely in bold R, and write your factorization using exact values (no approximations):

2x^3 + 5x ^2 -1

8. Factor completely in bold C, and write your factorization using exact values (no approximations):

x^4 -2x^3 -6x^2 +22x - 15

9. Write the equation of the parabola depicted in the graph illustrated below:

y-intercepts at (0,4) and (0, -4). Vertex at (2,0). Graph is sideways with two arms expanding to the left, vertex to the right at the x-intercept (2,0).

Thank you so much for your help!