1. QUADRATIC EQUATIONS MSJC ~ San Jacinto Campus
Math Center Workshop Series
Theresa Hert

2. Radicals with index 2 are referred to as square roots.
Simplify Radicals
Radicals with index 2 are referred to as square roots.

3. Simplify Radicals
Break down the radicand, the number inside the radical, into prime factors.
Circle a pair of matching factors,
take out THE factor.
Since no operation sign is visible, the “glue” holding everything together is Multiplication.
When you bring a factor out of the radical, it gets multiplied to the number in front of the radical.

4. Simplify the Radical

5. Simplify Rational Expressions containing Radicals
First simplify the radical.
To reduce the fraction, Factor.
Beware of addition.
Plus sign – use one set of parentheses to factor out what is common.

6. Simplify this Rational Expression containing a Radical

7. Quadratic Equations contain both an equal sign and
a variable with exponent 2.
General form: ax2 + bx + c = 0

8. A quadratic equation is an equation equivalent to an equation of the type
ax2 + bx + c = 0, where a is nonzero
We can solve a quadratic equation by using the Quadratic Formula

9. The Quadratic Formula
Solve the equation ax2 + bx + c = 0 for x by Completing the Square

10. The Quadratic Formula
Solutions to ax2 + bx + c = 0 for a nonzero are

11. Solve this Quadratic Equation by using the Quadratic Formula
6y2 – 3y – 5 = 0
a = 6 b = -3 c = -5

12. because of the addition,
6y2 – 3y – 5 = 0
a = 6 b = -3 c = -5
because of the addition,
you can NOT reduce the fraction

13. Ex: Use the Quadratic Formula to solve x2 + 7x + 6 = 01 7 6
Recall: For quadratic equation ax2 + bx + c = 0, the solutions to a quadratic equation are given by
Identify a, b, and c in ax2 + bx + c = 0:
a = b = c = 1 7 6
Now evaluate the quadratic formula at the identified values of a, b, and c

14. x2 + 7x + 6 = 0
a = 1 b = 7 c = 6
x = ( )/2 = - 1 and x = (-7 – 5)/2 = - 6
x = { - 1, - 6 }

15. Ex: Use the Quadratic Formula to solve
2m2 + m – 10 = 0 2 1
– 10
Recall: For quadratic equation ax2 + bx + c = 0, the solutions to a quadratic equation are given by
Identify a, b, and c in am2 + bm + c = 0:
a = b = c = 2 1
- 10
Now evaluate the quadratic formula at the identified values of a, b, and c

16. 2x2 + 1x – 10 = 0
a = 2 b = 1 c = -10
m = ( )/4 = 2 and m = (-1 – 9)/4 = - 5/2
m = { 2, - 5/2 }

17. Ex: Use the Quadratic Formula to solve
x2 + 5x = -3
x2 + 5x + 3 = 0 1
+ 5 3
Identify a, b, and c in ax2 + bx + c = 0:
a = b = c = 1
+ 5 3
Now evaluate the quadratic formula at the identified values of a, b, and c

18. x2 + 5x + 3 = a = 1 b = 5 c = 3

19. Ex: Use the Quadratic Formula to solve
10x2 – 5x = x2 – 5x + 0 = 0 10
- 5
Identify a, b, and c in ax2 + bx + c = 0:
a = b = c = 10
- 5
Now evaluate the quadratic formula at the identified values of a, b, and c

20. 10x2 – 5x + 0 = a = 10 b = -5 c = 0

21. Solve: use the Quadratic Formula.