Quadratic Functions Worksheets Grade 9

1. Mason is designing a custom skateboard ramp for a competition. The ramp's cross-section follows the path y = 2x² - 16x + 35, where y is the height in inches and x is the horizontal distance in feet from the starting point. What is the minimum height of the ramp in inches?
2. Emma is designing a custom frame for her art project. The frame's border follows the quadratic function y = 2x² - 12x + 19, where y represents the border width in centimeters at position x along the frame. What is the minimum width of the border in centimeters?
3. Matiu is designing a custom skateboard ramp. The shape of the ramp follows the quadratic function y = 2(x - 4)² + 6, where y represents the height in inches and x represents the horizontal distance in feet from the starting edge. To calculate the ramp's dimensions at ground level, Matiu needs to convert this equation to standard form. What is the coefficient of the x term in the standard form of this quadratic equation?

…and 4 more problems

1. Convert y = 4(x - 7)² + 9 to standard form y = ax² + bx + c
2. Mere is analyzing a quadratic function in vertex form: y = 2(x - 4)² + 6. She wants to convert it to standard form y = ax² + bx + c. What is the value of the coefficient b in the standard form?
3. Convert y = 2(x - 7)² + 9 to standard form

…and 6 more problems

1. Isabella is designing a custom frame for a painting. The frame's area can be modeled by the quadratic function A(w) = 3(w - 9)² + 48, where w is the width in inches. Convert this function to standard form A(w) = aw² + bw + c to determine the coefficient of the linear term.
2. Convert y = -3(x - 5)² + 10 to standard form
3. Convert y = 2(x - 4)² + 6 to standard form

…and 6 more problems