1. Chapter 4: Quadratic Functions and Equations
Section 4.7: The Quadratic Formula

2. Section 4.7: The Quadratic Formula
Goal: To solve quadratic equations using the Quadratic Formula and to determine the number of solutions by using the discriminant

3. Section 4.7: The Quadratic Formula
In this chapter, you have learned how to solve quadratic equations by factoring, isolating the variable, and completing the square
While completing the square will always work to solve a quadratic, it can be a “messy” process if there are fractions involved
Using the Quadratic Formula also always works for solving quadratics and may not involve “messy” fractions

4. Section 4.7: The Quadratic Formula
The Quadratic Formula: the equation must be in standard form before using the quadratic formula
If ax2 + bx + c = 0, then

5. Section 4.7: The Quadratic Formula
Examples:
1. Use the quadratic formula to solve: 5x2 – 2x = 2

6. Section 4.7: The Quadratic Formula
You try:
2. Solve x2 – 8x = 33 by using the Quadratic Formula

7. Section 4.7: The Quadratic Formula
You try:
3. Solve x2 – 34x +289 = 0 by using the Quadratic
Formula.

8. Section 4.7: The Quadratic Formula
Application:
4. You sell wrapping paper as a charity fundraiser. The equation p = -6x x – 1200 models the total profit p as a function of the price x per roll of paper. What is the smallest amount in dollars you can charge per roll of wrapping paper to make a profit of $1500?

9. Section 4.7: The Quadratic Formula
The Discriminant: b2 – 4ac (the stuff under the square root in the quadratic equation)
By evaluating the discriminant, the number or solutions and the type of solutions can be determined

10. Section 4.7: The Quadratic Formula
The Discriminant and the Solutions

11. Section 4.7: The Quadratic Formula
Examples:
5. What is the number of real solutions of
–x2 + 14x = 49 ?

12. Section 4.7: The Quadratic Formula
You try:
6. Find the value of the discriminant for each quadratic equation. Describe the number and type of roots for the equation.
A) x2 + 3x + 5 = 0
B) x2 – 11x + 10 = 0

13. Section 4.7: The Quadratic Formula
Application:
7. A rocket is launched from the ground with an initial vertical velocity of 150 ft/s. The function h = -16t t models the height in feet of the rocket at time t in seconds. Will the rocket reach a height of 300 ft? Explain your answer.

14. Section 4.7: The Quadratic Formula
Homework: Pg. 245 #12-38 (even)