1. 5.3 Discriminant and 5.4Find ABC Discriminant: b 2 – 4ac A, B, C ax 2 + bx + c = 0

2. 5.3 Discriminant and 5.4 Find ABC Always remember that MT5 revolves around the topic of this shape The graph of a Quadratic is called a Parabola Sometimes the shape can move around…

3. 5.3 Discriminant and 5.4 Find ABC The points where the line crosses the X Axis are called roots (zeros) Roots

4. 5.3 Discriminant and 5.4 Find ABC How many roots for each shape? A) B) C) A B C 0 1 2 Awesome Job!

5. 5.3 Discriminant and 5.4 Find ABC The Discriminant is a shortcut for finding out how many possible roots a parabola (graph of a quadratic) has without having to graph it. The formula is this… b 2 – 4ac We get our input from this equation… ax 2 + bx + c = 0

6. 5.3 Discriminant and 5.4 Find ABC Here’s what a problem will look like How many possible roots in this equation: 3x 2 + 4x - 5 4 2 – 4(3)(-5) Here’s how to solve: 3x 2 + 4x - 5 a b c A = 3 B = 4 C = -5 Now Plug It In! b 2 – 4ac

7. 5.3 Discriminant and 5.4 Find ABC Here’s what a problem will look like How many possible roots in this equation: 3x 2 + 4x - 5 4 2 – 4(3)(-5) Now solve: That’s it! 16 - – 60 16 + 60 76

8. 5.3 Discriminant and 5.4 Find ABC Here’s what a problem will look like How many possible roots in this equation: 3x 2 + 4x - 5 Finally: You must remember this part… Positive Answer: 2 Roots Zero (0): 1 Root Negative Answer: No Roots Your homework requires you to have three answers. In this problem your answer would be… A = 3 B = 476and2 roots C = -5

9. 5.3 Discriminant and 5.4 Find ABC Let’s practice the possible roots part… Please figure out how many possible roots 1. 25 2. - 18 3. 0 4. -6 2 roots (positive) No roots (negative) 1 root (zero) No roots (negative)