NOTES: QUADRATIC FORMULA
DAY 14
Textbook Chapter 4.8
OBJECTIVE:
Today you will learn about the quadratic formula and discriminant!
The Quadratic Formula: x =
−b ± b 2 − 4ac
2a
(a, b, c are real #’s) (a ≠ 0)
The Quadratic Formula can be used any time you are asked to find the
Roots, Zeros, or Solutions of a quadratic equation.
I.
Quadratic Equations with ________________________ Solutions
1) Put into standard form: Ax2 + Bx + C = 0
2) Identify a, b, and c.
3) Plug a, b and c into the quadratic formula. Solve for x. Reduce your square roots!
Use the Quadratic Formula to solve the Quadratic Equation!
2x2 + x – 5 = 0
II.
A = _____
B = _____
C = _____
Quadratic Equations with ________________________ Solutions
Use the Quadratic Formula to solve the Quadratic Equation!
x2 – 6x + 9 = 0
A = _____
B = _____
C = _____
III.
Quadratic Equations with _________________________ Solutions
Use the Quadratic Formula to solve the Quadratic Equation!
– x2 + 2x – 2 = 0
A = _____
B = _____
C = _____
…is used to determine the equation’s number and type of solutions.
The Discriminant
b2 – 4ac
-x2 + 2x = 2
x2 – 2x = 4x – 9
2x2 + 3x = 2x + 5
Pos Neg Zero
Pos Neg Zero
Pos Neg Zero
Put in
Standard Form
Find the
Discriminant
Number and
type of solutions
Sketch of graph
PRACTICE: QUADRATIC FORMULA
1.
x2 + 4x + 2 = 0
2.
3x2 + x – 3 = 0
3.
x2 – x – 20 = 0
4.
–x2 + 3x = 5
DAY 14
SOLVING QUADRATIC EQUATIONS: STANDARD FORM
Solving a quadratic function means to find the…
__________________, __________________, __________________, __________________,
Quadratic Function
(standard form)
y = x2 – x – 6
y = x2 – 9
y = –x2 + 3x + 6
SOLVE:
Find the Solutions
Quadratic Formula
Vertex: (
Zeros:
Solve by Graphing
on Calculator!
(use separate
instructions)
,
)
Vertex: (
Zeros:
,
)
Vertex: (
Zeros:
,
)
NAME: _____________________________________
Use the Quadratic Formula to solve the quadratic equations
1.
x2 + 14x + 1 = 0
2.
x2+ 5x + 4 = 0
3.
5x2 – 2 = –62
4.
2x2 + 5x = –3
DAY 14 DUE: ______
Solve using the quadratic formula.
5.
2x2 + 10x = 0
6.
4x2 + 12x = –9
Fill in the table!
Function
1. y = x2 – 8x + 17
2. y = x2 – 8x + 16
3. y = x2 – 8x + 15
4. y = x2 – 10x + 23
Discriminant
Number and
Type of
Solutions
Possible Graph