Transcript Quadratic Function

Quadratic Function
Finding the Solutions (roots) of a
Quadratic Function
by Graphing
Quadratic Function
(y = ax2 + bx + c)
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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
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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)
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When a is positive,
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When a is negative,
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When c is positive
When c is negative
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the graph opens
upward.
the graph opens
downward.
the graph moves up.
the graph moves
down.
What happens if b varies?
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Explore – Axis of Symmetry
x=-b/2a
The ‘b’ moves the AOS left/right
Solving Quadratic Functions
(ax2 + bx + c = 0)
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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)
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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
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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
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By factoring
By using the
quadratic formula
b  b  4ac
x
2a
2
The End