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