Download Section 1.6 solving quadratic equation

Section 1.6 Solving Quadratic Equations NOTES
Precalculus
A quadratic equation has a standard form of ax2 + bx + c = 0.
a.) For this equation, what letter represents the variable?
b.) For this equation, what letters represent the coefficients?
c.) For this equation, what letter represents the constant term?
d.) What is a root or solution of a quadratic equation?
Factoring:
Using Example 1 as a guide, solve (2x + 5) (x – 2) = -7 by factoring.
Completing the Square:
When completing the square, what does one side of the equation become?
Using Example 2 as a guide, solve 2x2 – 16x – 40 = 0 by completing the square.
The Quadratic Formula
What are the roots (solutions for x) for ax2 + bx + c = 0 as an equation:
Using Example 3 as a guide, solve 5x2 – 5x + 2 = 0 using the quadratic formula.
b  b2  4ac
:
2a
If b2 – 4ac is negative, will the result be real or imaginary?
Looking at the quadratic formula, x 
If b2 – 4ac is positive, will the result be real or imaginary?
If b2 – 4ac is not zero, will there be one or two solutions?
If b2 – 4ac is zero, will there be one or two solutions?
Choosing a Method of Solution
What formula can be used to solve any quadratic equation?
If a, b, and c are integers and b2 – 4ac is a perfect square, what is the best method
to use?
If the equation has the form x2 + (even number)x + constant = 0 what is the best
method to use?
Section 1.6 Solving Quadratic Equations Assignment
Precalculus
Solve by factoring.
1.) 3x2 – 4x – 7 = 0
2.) (2x – 3) (x + 4) = 6
For questions 3 – 5 solve by completing the square.
3.) x2 – 10x = 1575
4.) x2 + 6x + 10 = 0
5.) y2 + 10y + 35 = 0
For questions 6 – 10 solve using the quadratic formula.
6.) 5x2 + 2x – 1 = 0
7.) 3t2 = 12t – 15
8.) 5u2 + 2 = 5u
9.)
10.)
4 v6

v v4
4
3z

z z 3
For questions 11 – 13 solve by whichever method seems easiest. Give both real
and imaginary roots. Be sure not to lose or gain roots.
11.) 8x2 = 7 – 10x
12.) (4x + 7) (x – 1) = 2(x – 1)
t2 1 t
5
13.)
 
t2 3 t2
For problems 14 and 15, DE is parallel to BC . Find the value of x.
A
14.)
x
D
x+3
B
8
E
2x
C
A
15.)
x+6
D
6x
E
x
7x + 1
B
16.) For 4x2 + 8x + k = 0:
a.) What is the discriminant?
b.) For what values of k will the equation have a double root?
c.) For what values of k will the equation have two real roots?
d.) For what values of k will the equation have imaginary roots?
17.) Use the quadratic formula to solve ix2 – 3x – 2i = 0.
18.) Derive the quadratic formula (Hint: solve the general quadratic equation
ax2 + bx + c = 0, (a not equal to zero) by completing the square).
C