Quadratic Completing Square Worksheets Grade 9

1. The function f(x) = x² - 6x + 2 represents the height of a projectile in meters after x seconds. Find the time when the projectile reaches its minimum height by solving the equation x² - 6x + 2 = 0 using the completing the square method. Enter your answer as the exact value of x.
2. Sophia is designing a rectangular rooftop garden for an urban sustainability project. The length of the garden is 10 meters more than its width. The total area of the garden is 144 square meters. To determine if the design fits within the rooftop space, Sophia needs to find the exact dimensions. Set up a quadratic equation for the width (w) and solve it by completing the square to find the width and length of the garden.
3. Mason is designing a rectangular courtyard for a new community center. The length of the courtyard is 7 meters more than its width. The area of the courtyard is 98 square meters. To determine the exact dimensions, Mason writes an equation and solves it by completing the square. What are the width and length of the courtyard?

…and 3 more problems

1. x² + 6x - 7 = 0
2. Aroha is designing a rectangular community garden. The length of the garden is 9 meters more than its width. The area of the garden is 112 square meters. Aroha wants to know the exact width and length of the garden so she can order fencing. Use completing the square to find the width and length of the garden.
3. Emma is designing a rectangular flower bed for her school garden. The area of the flower bed can be modeled by the quadratic expression x² + 12x, where x represents the width in meters. To determine the dimensions that would make the flower bed a perfect square, Emma needs to rewrite the expression in vertex form by completing the square. What constant term must she add to x² + 12x to create a perfect square trinomial?

…and 4 more problems

1. Sophia is designing a rectangular mural for a community art project. The area of the mural is 108 square meters. The length is 6 meters more than twice the width. She needs to determine the exact dimensions to order the correct amount of paint. Set up a quadratic equation and solve it by completing the square to find the width and length of the mural.
2. A rectangular garden has a length that is 4 meters more than its width. If the area of the garden is 96 square meters, find the dimensions of the garden by writing and solving a quadratic equation using the method of completing the square.
3. Liam is designing a rectangular garden with a path around it. The garden area plus the path forms a larger rectangle that can be modeled by the quadratic expression x² + 8x. Liam needs to find what constant term should be added to this expression to create a perfect square trinomial, which would help him determine the original garden dimensions before the path was added. What constant completes the square for x² + 8x?

…and 4 more problems