Transcript 11.6 – Solving Quadratic Equations by Factoring

Quadratic Solutions
The number of real solutions is at
most two.
6
f  x  = x 2 -2 x +5
6
2
4
4
-5
2
5
2
-2
5
5
-4
-2
-2
No solutions
One solution
Two solutions
The solutions are located on the x axis, or the x value when
y=0. The solutions are sometimes called zeroes or roots
11.6 – Solving Quadratic Equations by Factoring
A quadratic equation is written in the Standard
Form,
2
ax  bx  c  0
where a, b, and c are real numbers and a  0.
Examples:
11.6 – Solving Quadratic Equations by Factoring
Zero Factor Property:
If a and b are real numbers and if ab  0 ,
then a  0 or b  0 .
11.6 – Solving Quadratic Equations by Factoring
Examples:
11.6 – Solving Quadratic Equations by Factoring
Solving Quadratic Equations:
11.6 – Solving Quadratic Equations by Factoring
11.6 – Solving Quadratic Equations by Factoring
If the Zero Factor
Property is not used,
then the solutions will
be incorrect
11.6 – Solving Quadratic Equations by Factoring
11.6 – Solving Quadratic Equations by Factoring
11.6 – Solving Quadratic Equations by Factoring
11.6 – Solving Quadratic Equations by Factoring
11.6 – Solving Quadratic Equations by Factoring
11.7 – Quadratic Equations and Problem Solving
A cliff diver is 64 feet above the surface of the
water. The formula for calculating the height (h)
2
of the diver after t seconds is: h  16t  64.
How long does it take for the diver to hit the surface
of the water?
11.7 – Quadratic Equations and Problem Solving
The square of a number minus twice the number is
63. Find the number.
11.7 – Quadratic Equations and Problem Solving
The length of a rectangular garden is 5 feet more than
its width. The area of the garden is 176 square feet.
What are the length and the width of the garden?
11.7 – Quadratic Equations and Problem Solving
Find two consecutive odd numbers whose product is
23 more than their sum?