Polynomial And Rational Functions
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- What is the form of a quadratic function?
- f(x)=ax^2+bx+c, a cannot = 0
- **What is the standard form of a quadratic function?
- f(x)= a(x-h)^2+k, a cannot equal 0
- What is the vertex of a parabola in the standard function?
- h,k
- What is the procedure for graphing a quadratic function?
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1. Determine if parabola opens upward or downward.
2. Determine the vertex of te parabola. The vertex is (h,k)
3. Find x intercepts by replacing f(x) with 0. Solve te quadratic equation.
4. Find the y intercept by replacing x with 0.
5. Plot the intercepts and the vertex an connect the dots. - Describe the graphs of polynomial functions.
- They are smooth and continuous.
- What does a>0 mean?
- The parabola opens upward.
- How do you find the x,y coordinates of the vertex of a parabola when the form of the quadratic function is in f(x)=ax^2+bx+c
- Substitute the numbers from the equation into x= -(b/2a) and solve for x.
- What is the quadratic formula?
- x= -b plus or minus the square root of b^2-4ac/ 2a
- If the degree is odd and the leading coefficieat is positive, describe the graph.
- The graph falls to the left and rises to the right.
- If the degree is odd and the leading coefficent is negative, describe the graph.
- The graph rises to the left and falls to the right.
- If the degree is odd and the leading coeffiecient is positive, describe the graph.
- The graph rises to the left and right.
- If the degree is even and the leading coefficient is negative, describe the graph.
- The graph falls to left and right.
- How do you find the zeros of f in a polynomial function?
- Set f(x) equal to zero and solve the resultant equation. The result will equal the x intercepts of the function at y=0.
- How many turning points will a polynomial function have?
- The number of the greatest exponent minus one turning points.
- What are the steps of graphing a polynomial fuction?
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1. Use the leading coefficent test to determine end behaviour.
2. Find the x-intercepts by setting f(x)=0
3. Find the y-intercept by computing f(0)
4. Use symmetry to help draw graph.
5. Check graph to determine if maximum number of turning points equals n-1.