Practice: Quadratic Functions and Equations Graphing a Quadratic Function , a i 1- Let f(2) = 222 4. (a) Idefy the coordinates of the vertex of f. (b) Does the graph 0f 1' Open up or open down? (Circle one.) (0) Sketch a graph of f on the axes provided. Include the v labeled with coordinates. ertex and at least 1 point on either (d) State the domain and range of I using interval notation. Domain: Range: 2. Let 9(2) = 3(:c - 1)2 +2. (21) Is the equation of g in standard form or vertex form? (Circle one.) (b) Identify the coordinates of the vertex of g. vertex (c) Does the graph of 9 open up or open down? (Circle one.) (d) Sketch a graph of g on the axes provided. Include the vertex and at least 1 point on either side of the labeled with coordinates. l7 (e) State the domain and range of g using interval notation. Domain: Range: Finding the Intercepts of a Quadratic Function 3. Let f(z) = 5x2 -6x -8. (a) Is the equation of f in standard form or vertex form? (Circle one.) (b) Find the y-intercept for the graph of f. (c) Find the r-intercept(s) for the graph of f. 4. Let f(I) = (I+3)2 -27. (a) Is the equation of f in standard form or vertex form? (Circle one.) (b) Find the y-intercept for the graph of f. (c) Find the r-intercept(s) for the graph of f. 185 Piecewise Functions Model 1: Income Tax any countries use income brackets and marginal tax rates to calculate income tax. The data in the following table approximately match the brackets and rates used by the United States in 2010. Bracket Income Range Marginal Tax Rate $0 - $8000 10% $8001 - $34,000 15% $34,001 - $82,000 25% The following diagram illustrates the calculation of income tax owed, using these rates, by an individual with taxable income of $44,000. $8,000 7 $34,000 $44,000 7 Gross: $10,000 $8,000 $26,000 $7,500 Net: $7,200 $22,100 $800 4 $3,900 $2,500 1. Why is the rectangle labeled Gross separated into three parts? 2. How were the three dollar values inside the Gross rectangle calculated? 3. What does the $800 grey rectangle represent? How was this value calculated? 4. What does the $3,900 grey rectangle represent? How was this value calculated? 5. What does the $2,500 grey rectangle represent? How was this value calculated?6. What is the total income tax owed by this person? 7. Suppose this individual instead had a taxable income of $48,000. Draw a diagram similar to the one in Model 1 and use it to calculate the income tax they owe. 8. Comparing your diagram in #8 with the one in Model 1, which values stayed the same and which changed? 9. Suppose a different individual has a taxable income of $28,000. (a) How much of this person's income falls into each income bracket? A : B : (b) Draw a diagram similar to the one in Model 1 and use it to calculate the income tax they owe.10. Suppose an individual's taxable income (1) is $8000 or less. (a) How much of this person's income falls into each income bracket? Hint: Two of your values should be constants, and one should depend on I. A : B : (b) Complete the formula for the tax owed by this person: T=. 11. Suppose an individual's taxable income (1) is more than $8,000 but less than $34,000. (a) How much of this person's income falls into each income bracket? Hint: Two of your values should be constants, and one should depend on I. A : B : C : (b) Complete the formula for the tax owed by this person: T = +. 12. Suppose an individual's taxable income (/) is more than $34,000 but less than $82,000. (a) How much of this person's income falls into each income bracket? Hint: Two of your values should be constants, and one should depend on I. A : B : C : (b) Complete the formula for the tax owed by this person: T = + 13. Write your formulas from #10, #11, and #12 in the appropriate places to create a single piecewise function that relates taxable income to income tax owed. if 0