1. SOLVE QUADRATIC EQUATIONS BY GRAPHING. 5.2 Solving Quadratic Equations by Graphing

2. Quadratic Equations Standard form of a quadratic equation ax² + bx + c = 0, where a ≠ 0 How to find solution(s) for quadratic equations. 1. Graphing x-intercept(s)- Where the graph crosses the x-axis. 2. Factoring- section 5.3 3. Square root-section 5.3 4. Quadratic Formula-section 5.6

3. Solutions of a Quadratic Equation A quadratic equation can have: 1 real solution2 real solutionsNo real solutions

4. Solve the equation by graphing EX) x² + 2x – 8 = 0 1) Set equation equal to zero and in descending order. 2) Graphing Calculator  Graph equation  [2 nd ] [Trace]  Zeros  Follow directions on calculator  If two x-intercepts follow the procedure twice.

5. Solve each equation by graphing 1) x² – x – 6 = 02) -x² + 4x – 1 = 0

6. Solve each equation by graphing 3) 10x = -25 – x² 4) 6x – x² = 10

8. Write a system of equations and solve 1) Find two real numbers with a sum of 8 and a product of 12. 2) Find two real numbers with a sum of 5 and a product of -14.

9. Solve the real world problem 3) An arrow is shot upward with a velocity of 64 feet per second. Ignoring the height of the archer, how long after the arrow is released does it hit the ground? Use the formula h(t) = v₀t – 16t², where h(t) is the height of an object in feet, v₀ is the objects initial velocity in feet per second, and t is the time in seconds.