Practice Problems. Lesson 5b - Solving Quadratic Equations
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1 1. Use your graphing calculator to help you determine the number type of solutions to each of the quadratic equations below. a) Begin by putting the equations into stard form. b) Drawn an accurate sketch of the parabola indicating the window you used. c) IF your solutions are real number solutions, use the graphing INTERSECT method to find them. d) Use proper notation to write the solutions the x-intercepts of the parabola. e) Label the x-intercepts on your graph. a) x 2 16x + 64 = 0 b) 5x 2 + 4x 5 = 0 Scottsdale Community College Page 207 Intermediate Algebra
2 c) 2x 2 4x = Solving Quadratic Equations by Factoring (GCF) a) Make sure the quadratic is in stard form b) Check if there is a common factor, other than 1, for each c) Write the left side in Completely Factored Form d) Set each linear factor to 0 solve for x e) Verify result by graphing f) Label the x-intercepts on your graph. g) Write final solutions (usually separated by a comma) a) 4x 2 8x = 0 Scottsdale Community College Page 208 Intermediate Algebra
3 b) 9x 2 + 6x = 0 c) 2x 2 = 4x 3. Use the Trial Error Factoring Method to solve each of the quadratic equations below. Verify your result by graphing the quadratic part of the equation looking at where it crosses the x-axis. Label the x-intercepts on your graph. a) Solve x 2 + 8x + 12 = 0 Scottsdale Community College Page 209 Intermediate Algebra
4 b) Solve x 2 x + 42 = 0 c) Solve 2x 2 3 = 5x d) Solve x 2-36 = 0 Scottsdale Community College Page 210 Intermediate Algebra
5 4. Use an appropriate factoring method to solve each of the quadratic equations below. Verify your result by graphing using the Intersection method. Label the x-intercepts on your graph. a) 9x x = 0 b) x x 24 = 0 c) 6x 2 + 7x + 2 = 0 Scottsdale Community College Page 211 Intermediate Algebra
6 5. Solve each quadratic equation by using the Quadratic Formula. a) Place your given quadratic equation in stard form. b) Identify the coefficients a, b, c c) Substitute these values into the quadratic formula below d) Simplify your result completely then check your solution graphically write your final solutions e) Label the x-intercepts on your graph. Quadratic Formula: x = b b 2 4ac 2a a) Solve 2x 2-2x - 4 = 0 (This one is a fill in the blank) Final solution x = -1, 2 (Be sure to verify graphically. Draw the graph label the intersects) Scottsdale Community College Page 212 Intermediate Algebra
7 b) 2x 2 5x = 4 c) 4x 2 2x = 6 Scottsdale Community College Page 213 Intermediate Algebra
8 6. Solve the quadratic equations, in the complex number system. Leave your final solution in the complex form a ± bi. Quadratic Formula: x = b b 2 4ac 2a a) (This one is a fill in the blank) Final solution: (Be sure to draw the graph label the y intersect) Scottsdale Community College Page 214 Intermediate Algebra
9 b) x 2 +2x+5=0 7. Farmer Treeman wants to plant four crops on his l, Cotton, Corn, Kelp Currants. He has 40,000 square feet for planting. He needs the length width of the property to be as shown in the picture below (measured in feet). He determines the equation for the area of his property is a. What will the length width of the property need to be? X Cotton Kelp 30 Currants Corn b. Determine the area of each section of the l. X 50 Scottsdale Community College Page 215 Intermediate Algebra
10 8. Simplify each of the following write in the form a + bi. To work with i on your calculator, press MODE then change REAL to a+bi by using your arrow keys. The i button is on the bottom row. a) (4 2i) 3(4 + 4i) = b) 6i(5 3i) = c) (3 i)(2 + i) = Scottsdale Community College Page 216 Intermediate Algebra
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