Warmup The Discriminant And the Quadratic Formula 9

Warm-up •

The Discriminant And the Quadratic Formula 9. 5 Day 1 Notes

Discriminant •

If the discriminant equals……. Number and Type of 2 real solutions Solutions Number of x -intercepts 1 real solutions No real solutions

Example 2 Use the related equation to find the number of x -intercepts of the graph of the function. Then match the equation to the graph. a) y = x 2 + 6 x + 3 b) y = x 2 + 6 x + 10 c) y = x 2 + 6 x + 9

Quadratic Formula • Notice that the discriminant is actually inside the quadratic formula!

Read/Say the formula as You can read this formula as: “x equals negative b plus or minus the square root of b squared minus 4 ac all over 2 a”

Steps to Solve: 1. Get the quadratic equation in standard form 2. Evaluate for the discriminant- how many and what type of solution do you have? 3. Continue quadratic formula.

Example 1 Solve x 2 + 5 x – 6 = 0 using the quadratic formula.

Example 2 Solve -3 x 2 + x = -5 using the quadratic formula.

Example 3 •

Homework Day 1 • Page 587: 4, 11 -13, 16, 17, 23

The Discriminant And the Quadratic Formula 9. 5 Day 2 Notes

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Example 1: •

Example 2 •

Example 3 Find the x-intercept of the graph of 4 x 2 – x – 7 = y

Exit Slip Solve the equation 4 x 2 + 5 x + 1 = 0

Homework Day 2 • Page 587: 18, 19, 26, 27, 31, 32, 34