Quadratic Vertex Form Worksheets Grade 10

1. Mere is designing a parabolic arch for a new garden entrance. The arch's shape is modeled by the quadratic function y = -2(x - 4)² + 18, where y is the height in meters above the ground and x is the horizontal distance in meters from the left edge of the arch. The local council requires that the highest point of the arch be at least 16 meters high for clearance. Determine the vertex of the arch and state whether it meets the council's height requirement.
2. Mere is designing a water fountain for a new park. The height of the water stream (in meters) above the fountain nozzle is modeled by the function h(d) = -0.04(d - 25)^2 + 30, where d is the horizontal distance (in meters) from the nozzle. The park committee wants to know the maximum height the water reaches and the horizontal distance from the nozzle where this occurs. What are these two values?
3. A quadratic function in vertex form is given by f(x) = 3(x + 4)^2 - 27. What is the minimum value of this function?

…and 4 more problems

1. Charlotte is an engineer designing a suspension bridge. The main cable of the bridge hangs in the shape of a parabola. The height of the cable above the bridge deck, in meters, is modeled by the function h(x) = 0.02(x - 40)² + 10, where x is the horizontal distance from the left tower in meters. The vertex of this parabola represents the lowest point of the cable. What is the horizontal distance from the left tower to the lowest point of the cable, and what is the height of the cable at that point?
2. Convert f(x) = 6x² - 36x + 51 to vertex form f(x) = a(x - h)² + k = ?
3. Convert f(x) = 4x² - 24x + 38 to vertex form f(x) = a(x - h)² + k = ?

…and 5 more problems

1. A drone is launched from a platform 12 meters high. Its height above ground is modeled by the function h(t) = -2t² + 8t + 12, where t is time in seconds. After how many seconds will the drone reach its maximum height?
2. Convert f(x) = 4x² - 24x + 35 to vertex form f(x) = a(x - h)² + k = ?
3. Convert f(x) = -4x² + 24x - 35 to vertex form f(x) = a(x - h)² + k = ?

…and 5 more problems