1. Quadratic Function
Lesson 5.1 Page 249

2. Quadratic Function
(y = ax2 + bx + c)




a, b, and c are called
the coefficients.
The graph will form a
parabola.
Each graph will have
either a maximum or
minimum point.
There is a line of
symmetry which will
divide the graph into
two halves.

3. y = x2



a = 1, b = 0, c = 0
Minimum point (0,0)
Axis of symmetry
x=0
y=x 2

4. What happen if we change the
value of a and c ?
y=3x2
y=-3x2
y=4x2+3
y=-4x2-2

5. Conclusion
(y = ax2+bx+c)




When a is positive,
When a is negative
When c is positive
When c is negative




the graph opens up
the graph opens
down
the graph moves up.
the graph moves
down.

6. What happens if b varies?

Explore

http://www.explorelearning.com/index.cfm?

Describe the changes in your own
words.

7. Solving Quadratic Functions
(ax2 + bx + c = 0)



Since y = ax2 + bx +c , by setting y=0
we set up a quadratic equation.
To find the solutions means we need to
find the x-intercept.
Since the graph is a parabola, there will
be two solutions.

8. To solve quadratic equations
(graphing method)




X 2 - 2x = 0
To solve the
equation, put y = x2-x
into your calculator.
Find the x intercept.
Two solutions, x=0
and x=2.
y=x2-2x

9. Find the Solutions
y=x2-4
y=-x2+5
y=x2+2x-15
y=-x2-1

10. Find the solutions
y=-x 2 +4x-1
y=x 2 +2x+1

11. Observations




Sometimes there are two solutions.
Sometimes there is only one solution.
Sometimes it is hard to locate the
solutions.
Sometimes there is no solution at all.

12. Other Methods


By factoring
By using the
quadratic formula
−b ± b − 4ac
x=
2a
2

13. The End