Algebra Tutorials!
Friday 23rd of March
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

## The Graph of f(x) = Ax2 + Bx + C

Example 1

The graph of y = 0.5x2 is shown. Assume that the coefficient of x2 for all three graphs is 0.5.

a. Find the equation of Parabola A.

b. Find the equation of Parabola B.

Solution

a. Parabola A is the graph of f(x) = 0.5x2 shifted down 4 units. So, it is the graph of the function f(x) = 0.5x2 - 4.

b. Parabola B is the graph of f(x) = 0.5x2 shifted up 2 units. So, it is the graph of the function f(x) = 0.5x2 + 2.

Example 2

Graph the functions:

a. f(x) = -x2

b. f(x) = -x2 + 4

c. f(x) = -x2 - 3

Solution

a. The function f(x) = -x2 has the same shape as f(x) = x2 but, because of the negative sign, it opens downward. To see this, we can calculate and plot a few ordered pairs.

 x f(x) = -x2 (x, y) -2-1 0 1 2 f(-2) = -(-2)2 = -4f(-1) = -(-1)2 = -1 f(0) = -(0)2 = 0 f(1) = -(1)2 = 1 f(2) = -(2)2 = -4 (-2, -4)(-1, -1) (0, 0) (1, -1) (2, -4)

b. The graph of f(x) = -x2 + 4 has the same shape as f(x) = -x2 but is shifted up 4 units.

c. The graph of f(x) = -x2 - 3 has the same shape as f(x) = -x2 but is shifted down 3 units.