Quadratic Equations
ADVERTISEMENT
1Math 4 Pre-Calculus
Name________________________
Date_________________________
Quadratic Equations — 2.3 & 2.4
General Form of a Quadratic Equation
a
2
a x
b x
c
0
0
Solving Quadratic Equations
Quadratic equations may be solved in various ways:
By factoring. This is the easiest way, IF it works! Get a zero on one side, factor, set each factor equal to zero and
solve.
2
By using the square root principle. If
x
d
, then x
d
. Use only if the equation is written (or can easily
2
be written ) in the form:
e x p r e s s i o n
c o n s t a n t
.
2
b
By completing the square. Get the variable terms on one side and the constant term on the other side. Add
2
to both sides of the equation. Rewrite the perfect square binomial. Solve using the square root principle.
By using the quadratic formula. The quadratic formula comes from completing the square on the general form of
a quadratic equation. Once derived, you can simply write any equation in standard form, plug in the values of a ,
2
b
b
4
a c
b , and c into the quadratic formula:
x
, and simplify to get the solutions to that equation.
2
a
Quadratic Formula and the Discriminant
2
The discriminant is the radicand of the Quadratic Formula. The discriminant,
b
4
a c
, indicates what kind of
solutions or roots (distinct, real, complex, etc.) the quadratic equation has.
Value of the Discriminant
Nature of Roots (Solutions)
2
b
4
a c
Positive
Two real distinct roots
Zero
One real repeated root
Negative
Two complex roots (complex conjugates)
Application
A farmer plans to enclose a rectangular region, using part of his barn for one side and fencing for the other three sides.
2
If the side parallel to the barn is to be twice the length of an adjacent side, and the area of the region is to be 128 ft
,
how many feet of fencing should be purchased?
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education