Transcript f(x)=ax2+bx+c - quadratickillers

By:
Chrystal Olerich
Austin Page
Stephanie Beeber
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Definition:
o Let n be a non-negative integer and let an, an-1,...a2, a1,
a0 be real numbers with an=0.
Examples of Polynomial Functions
o f(x)=ax+b
Linear Function
o f(x)=c
Constant Function
o f(x)=x2
Squaring Function
Don’t miss this
information!!
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Polynomial functions are classified by degree. Seconddegree polynomial functions are called quadratic funtions.
Definition:
o Let a, b, and c be real numbers with a=0.
o f(x)=ax2+bx+c
Examples:
o f(x)=x2+6x+2
o g(x)= 2(x-1)2-3
o h(x)=9+1/4x2
Don’t look
confused!
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The graph of a quadratic function is called a parabola. It is a
"U" shaped curve.
All parabolas are symmetric with respect to a line called the
axis of symmetry.
o The point where the axis intersects the parabola is the
vertex of the parabola.
Confused?!
Just ask questions! 
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f(x)=ax2+bx+c opens upward.
o Leading coefficient is positive.
f(x)=-ax2+bx+c opens downward.
o Leading coefficient is negative.
Vertex:
 If a>0, the vertex is the point with the minimum yvalue on the graph.
 If a<0, the vertex is the point with the maximum yvalue of the graph.
Don’t whine! If you
don’t get it, just listen
more!
Standard Form:
f(x)=a(x-h)2+k,
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a=0
The graph of f is a parabola whose axis is x=h and whose
vertex is the point (h,k).
No
snoozing!!
Example: Sketch the graph of f(x)=2x2+8x+7; identify the
vertex and the axis of the parabola.
Step 1: Write in standard form.
• f(x)=2x2+8x+7
2(x+2)2-1
o Opens upward, has a vertex at (-2,-1), is shifted
downward one unit and to shifted the left two units from
the graph y=2x2.
Step 2: To find x-intercepts of the graph of f(x)=ax2+bx+c,
you must solve the equation by factoring or the quadratic
formula.
If a bear can go
to the bathroom
you can
remember this!!
QUADRATIC FORMULA: x=-b
2a
b2-4ac
Graph:
4
3
2
1
Here to help!!
x=-2
y=x2
The vertex of the graph of f(x)=ax2+bx+c is:
-b, f -b
2a 2a
Example: Find the vertex of f(x)=x2+2x+4
-2, f -b
(-1/2)2+4(-1/2)+3=1 1/4
4
2a
Ready to
Vertex: (-1/2, 1 1/4)
put this
knowledge
to use!