Quadratic Function
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Transcript Quadratic Function
Quadratic Function
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 concaves
downward.
the graph concaves
upward.
the graph moves up.
the graph moves
down.
What happens if b varies?
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Describe the changes in your own
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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+5
y=x2+2x-15
y=-x2-1
Find the solutions
y=-x2+4x-1
Observations
Sometimes
Sometimes
Sometimes
solutions.
Sometimes
there are two solutions.
there is only one solution.
it is hard to locate the
there is no solution at all.
Other Methods
By factoring
By using the
quadratic formula
b b 4ac
x
2a
2
The End