Name___________________________________________________ 32.3: Quadratic Formula Homework Algebra #1-2: State the value of the discriminant for each equation. Then determine the number of real solutions of the equation. 5 3 2 3 = x 1. 2x 2 = x + 2. x 2 + 2 2 25 5 #3-4: Find the sign of the discriminant and the number of roots using the graph. 3. 4. #5-7: Solve each equation using the Quadratic Formula. Round to the nearest hundredth if necessary. 5. 81x 2 = 9 6. 4 x 2 = −16 x − 16 7. −3x 2 = 8 x − 12 #8-10: Solve each equation using the Quadratic Formula. Round to the nearest hundredth if necessary. 2 8. 3x = −6 x + 4 9. x 2 + 3x = −x + 1 10. 2x 2 + 3x = 5 11. The equation d = 0.05v 2 + 1.1v models the distance d in feet it takes a car traveling at a speed of v miles per hour to come to a complete stop. The speed limit on some highways is 65 miles per hour. If Hannah’s car stopped after 250 feet, was she speeding? Explain your reasoning. 12. CRITIQUE THE REASONING OF OTHERS. José and Marta each solved x 2 + 4 x = −3 , but each used a different method. Who is correct and what is the error in the other student’s work?

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