1. Goal: Graph quadratic functions in the form y = ax 2 + bx + c

2. Warm-Ups Find the x – intercept and the y – intercept: 1. 3x – 5y = 15 x – intercept: 5 y – intercept: -3 2. y = 2x + 7 x – intercept: -7/2 y – intercept: 7

3. Quadratic Function A function that can be written in the standard form y = ax 2 + bx + c where a ≠ o The graph of a quadratic function is a parabola The graph of y = x 2 :

4. Steps to Solving a Quadratic Function Using a Table Step 1: Make a table of values. Step 2: Plot the points from the table. Step 3: Draw a smooth curve through the points.

5. Example 1: Graph a Quadratic Function Using a Table Graph: y = ½x 2 – 1 X-4-2024 Y

6. Checkpoint: Graph a Quadratic Function Using a Table Graph: y = -3x 2 X-2012 Y

7. Checkpoint: Graph a Quadratic Function Using a Table Graph: y = -x 2 – 2 X-2012 Y

8. Checkpoint: Graph a Quadratic Function Using a Table Graph: y = ¼ x 2 + 3 X-4-2024 Y

10. Example 2: Graph a Quadratic Function in Standard Form y = x 2 – 6x + 5

11. Example 2: Graph a Quadratic Function in Standard Form y = -x 2 – 2x + 1

12. Example 2: Graph a Quadratic Function in Standard Form y = 2x 2 + x - 1

13. Multiplying Binomials Monomial – a number, a variable or the product of a number and one or more variables with whole number exponents. Binomial – the sum of two monomials The FOIL is used to multiply binomials: First terms Outer terms Inner terms Last terms

14. Example 3: Multiply Binomials Find the product (2x + 3)(x – 7).

15. Checkpoint: Find the product. a. (x – 4)(x + 6) b. (3x + 1) (x – 1)

16. Example 4: Write a Quadratic Function in Standard Form Write the function y = 2(x – 2) 2 + 5

17. Checkpoint: Write the function in standard form. a. y = 2(x + 1)(x – 3) b. Y = 3(x – 4) (x – 6)

19. p. 225 – 227 16 – 64 even, 71 – 74 all