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Polynomial functions are classified by degree. Second- degree 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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By:Chrystal OlerichAustin PageStephanie Beeber
• 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 Functiono f(x)=c Constant Functiono f(x)=x2 Squaring Function
Don’t miss this information!!
• Polynomial functions are classified by degree. Second-degree 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+2o g(x)= 2(x-1)2-3o h(x)=9+1/4x2
Don’t look confused!
• 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!
• 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 y-
value on the graph. If a<0, the vertex is the point with the maximum y-
value of the graph.Don’t whine! If you don’t get it, just listen more!
Standard Form: f(x)=a(x-h)2+k, 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.
QUADRATIC FORMULA: x=-b b2-4ac 2a
If a bear can go to the
bathroom you can remember
this!!
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
Vertex: (-1/2, 1 1/4)
Ready to put this
knowledge to use!
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