Quadratic Function
Lesson 5.1 Page 249
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.
y = x2
a = 1, b = 0, c = 0
Minimum point (0,0)
Axis of symmetry x=0
y=x2
What happen if we change the value of a and c ?
y=3x2
y=-3x2
y=4x2+3
y=-4x2-2
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.
What happens if b varies? Explore
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=154
Describe the changes in your own words.
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.
To solve quadratic equations(graphing method) X2 - 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
Find the Solutions
y=x2-4 y=x2+2x-15
y=-x2+5 y=-x2-1
Find the solutions
y=x2+2x+1
y=-x2+4x-1
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.
Other Methods
By factoring
By using the quadratic formula 2 4
2
b b acx
a
The End