By: Chrystal Olerich Austin Page Stephanie Beeber.

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Presentation transcript:

By: Chrystal Olerich Austin Page Stephanie 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 Function o f(x)=c Constant Function o 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+2 o g(x)= 2(x-1)2-3 o 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!!

Graph: x=-2 y=x Here to help!!

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!