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MAC1106 Lecture Notes - Lecture 13: Quadratic Equation

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10 Jan 2018

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Miami Dade College

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Mathematics: Calculus & Pre-Calculus

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Document Summary

4. 3 quadratic functions and their properties notes: sterling. Provide a generalization to the terms listed in this section. What are intercepts: intercepts are points on a graph where the points touch or cross the coordinate axes, there are three di erent types of intercepts: X-intercepts are points on a graph where the points cross or touch the x-axis. Y -intercepts are points on a graph where the points cross or touch the y-axis. The origin is the only point on a graph where the point crosses or touches both the x-axis and y-axis. How do you nd the intercepts: x-intercepts. Substitute 0 for y, which is f (x). Solve for the x variable: y -intercepts. Intercepts example f (x) = x2 3x + 4. Y intercept(s) y = 02 3(0) + 4 y = 0 0 + 4 (0, 4)

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Related Questions

Algebra

Complete the square of the given quadratic expression. Then, graph the function using the technique of shifting. f(x) = x2 -6x + 8 Complete the square by entering the correct numbers into the expression below. f(x) = (x-( ))2 + ( ) Choose the correct graph below. The function f is defined as follows. Find the domain of the function. Locate any intercepts. Graph the function. Based on the graph, find the range. Is f continuous on its domain? The domain of the function f is (Type your answer in interval notation.) Locate any intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The intercept(s) is/are . (Type an ordered pair. Use a comma to separate answers as needed.) There are no intercepts. Choose the correct graph of the function below. The range of the function f is (Type your answer in interval notation.) Is f continuous on its domain? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Yes, f is continuous on its domain. No, f is discontinuous at x = . (Use a comma to separate answers as needed.) The function f is defined as follows. Find the domain of the function. Locate any intercepts. Graph the function. Based on the graph, find the range. Is f continuous on its domain? The domain of the function f is (Type your answer in interval notation.) Locate any intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) There are no intercepts. Choose the correct graph of f(x) below. The range of the function f is (Type your answer in interval notation.) Is f continuous on its domain? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. No, f is discontinuous at x = |. (Use a comma to separate answers as needed.) Yes, f is continuous on its domain. Find the distance d(P1 P2) between the given points P1 and P2. P1 =(-5,2) P2 = (4.4) d(P1, P2) = (Simplify your answer. Type an exact answer, using radicals as needed.) Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set. Choose the correct answer below that is the solution set to the inequality. Choose the correct graph below that is the solution set to the inequality. Determine whether the graph below is that of a function by using the vertical-line test. If it is, use the graph to find its domain and range. the intercepts, if any. any symmetry' with respect to the x-axis, y-axis, or the origin. Is the graph that of a function? Yes No If the graph is that of a function, what are the domain and range of the function? Select the correct choice below and fill in any answer boxes within your choice. The domain is The range is (Type your answers in interval notation.) The graph is not a function. What are the intercepts? Select the correct choice below and fill in any answer boxes within your choice. The graph of an equation is given. List the intercepts of the graph. Based the graph, tell whether the graph is symmetric with the respect to the x-axis, y-axis, and/or the origin What are the intercept(s) of the graph? Select the correct choice below and fill in any answer boxes within your choice. The intercept(s) of the graph are (Type an ordered pair. Use a comma to separate answers as needed.) There are no intercepts. Determine if the graph is symmetric. It is symmetric with respect to the x-axis. It is symmetric with respect to the y-axis. It is symmetric with respect to the origin. The graph is not symmetric. Solve the following inequality. Graph the solution set. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The solution set is (Type your answer in interval notation.) There is no real solution. Graph the solution set. Choose the correct graph below. Determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find its domain and range. the intercepts, if any. any symmetry with respect to the x-axis, y-axis, or the origin. Is the graph that of a function? Yes No What are the domain and range of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The domain is . The range is . (Type your answers in interval notation.) The graph is not that of a function. What are the intercepts of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Find the real solutions, it any. ot the following equation. Use the quadratic formula. Select the correct choice below and, if necessary, fill in the answer box to complete your answer. The solution set is . (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) The solution is not a real number.

Show transcribed image text Complete the square of the given quadratic expression. Then, graph the function using the technique of shifting. f(x) = x2 -6x + 8 Complete the square by entering the correct numbers into the expression below. f(x) = (x-( ))2 + ( ) Choose the correct graph below. The function f is defined as follows. Find the domain of the function. Locate any intercepts. Graph the function. Based on the graph, find the range. Is f continuous on its domain? The domain of the function f is (Type your answer in interval notation.) Locate any intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The intercept(s) is/are . (Type an ordered pair. Use a comma to separate answers as needed.) There are no intercepts. Choose the correct graph of the function below. The range of the function f is (Type your answer in interval notation.) Is f continuous on its domain? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Yes, f is continuous on its domain. No, f is discontinuous at x = . (Use a comma to separate answers as needed.) The function f is defined as follows. Find the domain of the function. Locate any intercepts. Graph the function. Based on the graph, find the range. Is f continuous on its domain? The domain of the function f is (Type your answer in interval notation.) Locate any intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) There are no intercepts. Choose the correct graph of f(x) below. The range of the function f is (Type your answer in interval notation.) Is f continuous on its domain? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. No, f is discontinuous at x = |. (Use a comma to separate answers as needed.) Yes, f is continuous on its domain. Find the distance d(P1 P2) between the given points P1 and P2. P1 =(-5,2) P2 = (4.4) d(P1, P2) = (Simplify your answer. Type an exact answer, using radicals as needed.) Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set. Choose the correct answer below that is the solution set to the inequality. Choose the correct graph below that is the solution set to the inequality. Determine whether the graph below is that of a function by using the vertical-line test. If it is, use the graph to find its domain and range. the intercepts, if any. any symmetry' with respect to the x-axis, y-axis, or the origin. Is the graph that of a function? Yes No If the graph is that of a function, what are the domain and range of the function? Select the correct choice below and fill in any answer boxes within your choice. The domain is The range is (Type your answers in interval notation.) The graph is not a function. What are the intercepts? Select the correct choice below and fill in any answer boxes within your choice. The graph of an equation is given. List the intercepts of the graph. Based the graph, tell whether the graph is symmetric with the respect to the x-axis, y-axis, and/or the origin What are the intercept(s) of the graph? Select the correct choice below and fill in any answer boxes within your choice. The intercept(s) of the graph are (Type an ordered pair. Use a comma to separate answers as needed.) There are no intercepts. Determine if the graph is symmetric. It is symmetric with respect to the x-axis. It is symmetric with respect to the y-axis. It is symmetric with respect to the origin. The graph is not symmetric. Solve the following inequality. Graph the solution set. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The solution set is (Type your answer in interval notation.) There is no real solution. Graph the solution set. Choose the correct graph below. Determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find its domain and range. the intercepts, if any. any symmetry with respect to the x-axis, y-axis, or the origin. Is the graph that of a function? Yes No What are the domain and range of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The domain is . The range is . (Type your answers in interval notation.) The graph is not that of a function. What are the intercepts of the function? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Find the real solutions, it any. ot the following equation. Use the quadratic formula. Select the correct choice below and, if necessary, fill in the answer box to complete your answer. The solution set is . (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) The solution is not a real number.

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Algebra

The function f(x) = 4x/9x-7 is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Graph the function. Based on the graph, state the domain and the range and find any intercepts. The domain is . (Type your answer in interval notation.) The range is . (Type your answer in interval notation.) Find the intercepts, if there are any. Select the correct choice below and fill in any answer boxes within your choice. The intercept(s) is'are . (Type an ordered pair. Use a comma to separate answers as needed. Type an exact answer.) Solve the equation. What is the solution? x = (Use a comma to separate answers.) If f(x) = 5x2 + 3 and g(x) = 9x + a, find a so that the graph of f g crosses the y-axis at 8. What is the value of a? a = (Use reduced fractions or integers. Use commas to separate values.) The function f(x) = 7/4+x is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Suppose that H(x) = (1/4)x - 4096 What is H( - 5)? What is the point that corresponds to this vahie on the graph of H? If H(x) = - 4032, what is x? What is the point that corresponds to this vahie on the graph of H? Find the zero of H. H( - 5) = (Type an integer or a simplified fraction.) The point that corresponds to this vahie on the graph of H is . (Type an ordered pair, but do not use commas in any individual coordinates.) If H(x) = - 4032, then x = . (Type an integer or a simplified fraction.) The point that corresponds to this vahie on the graph of H is . (Type an ordered pair, but do not use commas in any individual coordinates.) The zero of H is x = (Type an integer or a simplified fraction.) If f(x) = x3 - 3x2 + 2x - 9 and g(x) = 4: find (f g)(x) and (g f)(x). What is (f g)(x)? What is (f g)(x)? (f g)(x) = What is (g f)(x)? (g f)(x) = The function f(x) = 8x/x+5 is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Solve the equation. ex= e9x + 72 x = (Use a comma to separate answers as needed.)

Show transcribed image text The function f(x) = 4x/9x-7 is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Graph the function. Based on the graph, state the domain and the range and find any intercepts. The domain is . (Type your answer in interval notation.) The range is . (Type your answer in interval notation.) Find the intercepts, if there are any. Select the correct choice below and fill in any answer boxes within your choice. The intercept(s) is'are . (Type an ordered pair. Use a comma to separate answers as needed. Type an exact answer.) Solve the equation. What is the solution? x = (Use a comma to separate answers.) If f(x) = 5x2 + 3 and g(x) = 9x + a, find a so that the graph of f g crosses the y-axis at 8. What is the value of a? a = (Use reduced fractions or integers. Use commas to separate values.) The function f(x) = 7/4+x is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Suppose that H(x) = (1/4)x - 4096 What is H( - 5)? What is the point that corresponds to this vahie on the graph of H? If H(x) = - 4032, what is x? What is the point that corresponds to this vahie on the graph of H? Find the zero of H. H( - 5) = (Type an integer or a simplified fraction.) The point that corresponds to this vahie on the graph of H is . (Type an ordered pair, but do not use commas in any individual coordinates.) If H(x) = - 4032, then x = . (Type an integer or a simplified fraction.) The point that corresponds to this vahie on the graph of H is . (Type an ordered pair, but do not use commas in any individual coordinates.) The zero of H is x = (Type an integer or a simplified fraction.) If f(x) = x3 - 3x2 + 2x - 9 and g(x) = 4: find (f g)(x) and (g f)(x). What is (f g)(x)? What is (f g)(x)? (f g)(x) = What is (g f)(x)? (g f)(x) = The function f(x) = 8x/x+5 is one-to-one. Find its inverse and check your answer. f -1 (x) = (Simplify your answer.) Solve the equation. ex= e9x + 72 x = (Use a comma to separate answers as needed.)

Algebra

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