Quadratic Functions Praxis

Use the Zero-Factor Property to find all solutions to the given equations

1. \((x-2)(x+3)=0\)
2. \((2x+1)(-3x-2)=0\)
3. \(x\cdot (x+2)\cdot (4x-2)=0\)
4. \(x^2\cdot (x+1)^2=0\)
5. \(x^2=2x+1=0\)
6. \(15x^2+7x-2=0\)
7. \(12x^2-14x=-4\)
8. \(x^2=x+6\)

Honors Problem 1. \((3x+1)^2=2(3x+1)-1\)

Use the square root property to solve the following equations. Don’t be surprised if some of your answers are imaginary.

9. \(9x^2-1=0\)
10. \(5x^2-2=0\)
11. \(x^2+2=0\)
12. \((x-2)^2=4\)
13. \((4x+1)^2-3=2\)
14. \(2(x-1)^2+7=9\)

Use the quadratic formula to solve the following equations. Show how you plugged your numbers in. Feel free to compare your answers with that of a calculator.

15. \(x^2+5x-3=0\)
16. \(4x^2-4x+7=0\)
17. \(3.14x^2-4.21x+1=0\)
18. \(2.71x^2=0.78x-1.21\)
19. \(8.57x^2+0.01=0.28x-5.1\)
20. \(5x^2-2.3x+4=3.2x^2+5\)