1. Quadratic Equations and Quadratic Functions

2. Vocabulary
Quadratic function-
Quadratic term-
Linear term-
Constant term-
Parabola- the graph of a quadratic function
Axis of Symmetry- a line that makes the parabola symmetric
Vertex- the minimum or maximum point of the parabola
Zeros- the x-intercepts of the parabola

3. Identify the quadratic term, the linear term, and the constant term.
1) ) 3)

4. Solving Quadratic Equations by Factoring
Objective:
1) To solve problems by factoring

5. Solve by using he zero product property by factoring
1) 2) 3)

6. The Quadratic Formula and the Discriminant
Objective:
To solve quadratic equations by using the quadratic formula
To use the discriminant to determine the nature of the roots of quadratic equations

7. Quadratic Equations
ax2+bx+c=0
Solve by:
The Quadratic formula

8. Quadratic Functions Vertex form General Form Axis of symmetry is
Vertex is
a>0 parabola opens up
and has minimum
a<0 parabola opens down
and has maximum
|a|>1 parabola is narrow
|a|<1 parabola is wide
Axis of symmetry is x=h
Vertex is (h,k)
a>0 parabola opens up
and has minimum
a<0 parabola opens down
and has maximum
|a|>1 parabola is narrow
|a|<1 parabola is wide
and solve

9. Use quadratic formula to solve each equation.
(1.)

10. Use quadratic formula to solve each equation.
(2.)

11. Discriminant a Perfect Square?
Examples
Value of
Discriminant a Perfect Square?
Nature of Roots 1
Greater than zero
Yes
2 real, rational #’s 2
2 real,
Irrational #’s 3
Less than zero na
2 imaginary #’s 4
Zero
1 real #

12. Find the value of the discriminant for each quadratic equation
Find the value of the discriminant for each quadratic equation. Then describe the nature of the roots.
3) 4)

13. Find the value of the discriminant for each quadratic equation
Find the value of the discriminant for each quadratic equation. Then describe the nature of the roots.
5) 6)

14. Vertex to Standard Form
Notes

15. Change quadratic functions to standard form
Rewrite (x+1)²
Multiply using FOIL
Don’t forget your +2
Combine like terms
Standard Form

16. Compare Vertex vs. Standard
Standard form:
Vertex form:
Lets look at our last problem
We converted to
a = 1
b = 2
c = 3
a = 1
h = -1
k = 2
Compare values

17. Lets try this one!
Write the quadratic function in standard form. Label the values for a, b, and c.

18. Your Turn
Write the quadratic function in standard form. Label the values for a, b, and c.