Download 7.2 and 7.3 Quadratic Formula and Discriminant Printable

7.2/7.3
The Discriminant &
Quadratic Formula
Learning goal
Solve quadratic equations by inspection (e.g., for x² = 49),
taking square roots, completing the square, the
quadratic formula and factoring, as appropriate to the
initial form of the equation. Recognize when the
quadratic formula gives complex solutions and write
them as a ± bi for real numbers a and b.
If a quadratic equation is written
in standard form ax2  bx  c  0
then it can be solved with the
Quadratic Formula
b  b  4ac
x
2a
2
discriminant : value beneath the radical
determines # and type of solutions
2
b  4 ac
Value of
Discriminant
>0
and a
perfect square
>0
and NOT a
perfect square
Number
of
Solutions
Type of
Solutions
Graph Intercepts
___ x-intercepts
___ x-intercepts
=0
___ x-intercept
<0
___ x-intercepts
Graph
Ex 1
Determine the type & number of solutions.
x  5 x  10  0
2
x  6x  9  0
2
Ex 2
Determine the type & number of solutions.
x  5x  5  0
2
5x  5x  1  0
2
Ex 3
Solve using the QF
3 x  23 x  40  0
2
Ex 4
Solve using the QF
3 x  2 x  4
2
Ex 5
A swimming pool 6 m wide and 10 m long is to be surrounded by
a walk of uniform width. The area of the walk happens to be
equal to the area of the pool. What is the width of the walk?
(Hint: Draw a diagram 1st)