Quadratic Function

1
Quadratic Function
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 x0

yx2
4
What happen if we change the value of a and c ?
y3x2
y4x23
y-4x2-2
y-3x2
5
Conclusion(y ax2bxc)

• When a is positive,
• When a is negative,
• When c is positive
• When c is negative

• the graph concaves downward.
• the graph concaves upward.
• the graph moves up.
• the graph moves down.

6
What happens if b varies?

• Explore
• http//www.explorelearning.com/index.cfm?methodcR
  esource.dspViewResourceID154
• Describe the changes in your own words.

7
Solving Quadratic Functions(ax2 bx c 0)

• Since y ax2 bx c , by setting y0 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)

• X2 - 2x 0
• To solve the equation, put y x2-x into your
  calculator.
• Find the x intercept.
• Two solutions, x0 and x2.

yx2-2x
9
Find the Solutions
yx2-4
yx22x-15
y-x25
y-x2-1
10
Find the solutions
y-x24x-1
yx22x1
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

13
The End