Factor Quadratics Worksheets Grade 9

1. A local theater is designing a new stage backdrop that will have a rectangular opening for special effects. The area of the opening is given by the quadratic expression 3x² + 10x + 8 square feet, where x represents the additional length beyond the minimum dimensions. The theater director knows that the width of the opening is (x + 2) feet. What expression represents the length of the opening in factored form?
2. A rectangular garden has a length that is 3 meters more than twice its width. The area of the garden is 65 square meters. If you were to draw this garden on a coordinate plane with one corner at the origin and the sides along the axes, what would be the dimensions of the rectangle?
3. A right triangle is drawn on a coordinate plane with vertices at (0,0), (x,0), and (0,x-3). The area of the triangle is 14 square units. Write the quadratic equation in standard form that represents the relationship between x and the given conditions.

…and 5 more problems

1. A physics class is designing a projectile motion experiment where the height of a ball thrown upward is modeled by the function h(t) = -16t² + 64t + 80, where h is the height in feet and t is the time in seconds. The teacher asks students to factor this quadratic expression to determine at what time the ball will hit the ground. What is the factored form of the height function?
2. A physics student is designing a parabolic arch for a model bridge. The arch's height above ground is modeled by the function h(x) = -2x² + 12x - 16, where x represents the horizontal distance from the left support in meters. Factor this quadratic expression to determine at what horizontal distances from the left support the arch touches the ground.
3. A rectangular garden has an area represented by the expression 2x² + 7x + 6 square meters. If the length of the garden is (2x + 3) meters, what expression represents the width of the garden in meters?

…and 5 more problems

1. A physics student is analyzing the trajectory of a rocket launched from ground level. The height of the rocket above the ground is modeled by the quadratic function h(t) = -5t² + 40t, where h is the height in meters and t is the time in seconds after launch. Factor this quadratic expression to determine at what time the rocket will return to the ground.
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (x,0), and (0,x+3). The area of the triangle is 20 square units. Write the quadratic equation in standard form that represents the relationship between x and the given conditions.
3. Factor completely: 8x² - 22x + 12 = ?

…and 5 more problems