4.8 “The Quadratic Formula”The Quadratic Formula is used to find solutions for the equation:

ax2 + bx + c = 0

x =

Steps:1. Get the equation in the

correct form.

2. Identify a, b, & c.

3. Plug numbers into the formula.

4. Solve, then simplify if possible.

I. Equations With Two Real SolutionsReal Numbers: , Find the solutions to the following quadratic equations:

1. x2 + 3x = 2

2. x2 – 5x = 7

II. Equations With One Real SolutionFind the solutions to the following quadratic equations:

3. 25x2 – 18x = 12x – 9

4. 16x2 – 23x = 17x – 25

III. Equations With Imaginary SolutionsFind the solutions to the following quadratic equations:

5. – x2 + 4x = 5

6. 4x2 + 3x + 12 = 3 – 3x

Try These 7. 7x2 – 2x = 5 8. – 5x2 + 3x + 1 = 6 – 7x