Completing the Square Worksheets Grade 10

1. Complete the square: x² + 16x + 61 = 0 → (x + a)² = b, find a and b?
2. x² - 8x + 13 = 0 → (x - h)² = k, find k?
3. Noah is designing a parabolic arch for a bridge. The arch is drawn on a coordinate plane, with the base of the arch on the x-axis from x = 0 to x = 6. The height of the arch at any point x is given by the quadratic function h(x) = -x² + 6x. By completing the square, find the vertex form of this function and determine the maximum height of the arch.

…and 4 more problems

1. Olivia is designing a parabolic water slide for a new amusement park. The height of the slide (in meters) above the ground is given by the quadratic function h(x) = -3x² + 27x - 51, where x is the horizontal distance (in meters) from the starting platform. Using the method of completing the square, rewrite the function in vertex form h(x) = a(x - p)² + q to determine the maximum height of the slide and the horizontal distance from the start where this maximum occurs. Then, state the coordinates of the vertex.
2. A projectile's height above ground is modeled by the equation h(t) = -16t² + 96t + 112, where h is height in feet and t is time in seconds. By completing the square, determine the maximum height the projectile reaches.
3. Complete the square: x² - 12x + 35 = 0 → (x - h)² = k, find h and k?

…and 5 more problems

1. Complete the square: 3x² - 30x + 72 = 0 → (x + a)² = b, find a and b?
2. Complete the square: 2x² - 16x + 10 = 0 → (x + a)² = b, find a and b?
3. Complete the square: 2x² + 12x + 10 = 0 → (x + h)² = k, find h and k?

…and 4 more problems