Section 5.8 The Quadratic Formula Obj: to solve quadratic equations using the quadratic formula Obj: to use the discriminant to state the number and nature of solutions to a quadratic equation

Y = a 𝑥 2 + bx + c Quadratic Formula: 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 Discriminant: 𝑏 2 −4ac Tells you what type and how many solutions you can expect to get from your equation

Discriminant: 𝑏 2 −4ac The discriminant tells you how many and what type (nature) of solutions to expect from your equation. If 𝑏 2 −4ac is positive, then your equation will have 2 real solutions. If 𝑏 2 −4ac = negative, then your equations will have 2 imaginary solutions. If 𝑏 2 −4ac = 0, then your equation will have 1 real solution.

Ex 1 3 𝑥 2 - 5x -2 = 0

Ex 2 3 𝑥 2 - x = 4

Ex 3 2 𝑥 2 = -6x - 7

Ex 4 -2 𝑥 2 = 4x + 3

Assign: Pg. 289 column 1 Solve using the quadratic formula Use the discriminant to predict the number and nature of the solutions.