Grade 10 Quadratic Relations Worksheets
Free printable quadratic relations practice for Grade 10 students. Generate problems, solve them on screen or paper, and download as PDF.
What your child will practice
- Quadratic Relations from TablesIdentify quadratic relations by examining second differences in tables of values.
- Properties of ParabolasIdentify the key features of a parabola (vertex, axis of symmetry, zeros, direction of opening).
- Factoring QuadraticsFactor polynomial expressions involving common factors, trinomials, and differences of squares.
- Solving by FactoringSolve quadratic equations by factoring and relate solutions to x-intercepts of the graph.
- Completing the SquareSolve quadratic equations by completing the square.
Free Practice Worksheets
Print, solve on paper, then upload a photo for instant AI grading and feedback.
Build confidence with approachable problems
Solve each problem. Take your time.
- 1.Identify the vertex of the parabola represented by the equation y = (x - 3)² + 5.
- 2.Factor the quadratic expression: x² + 7x + 10.
- 3.Find the axis of symmetry for the parabola y = 2x² - 8x + 1.
- 4.Rewrite the quadratic equation y = x² + 6x + 2 in vertex form y = a(x-h)² + k.
- 5.Use the quadratic formula to find the roots of the equation x² - 5x + 6 = 0. The formula is x = [-b ± √(b² - 4ac)] / 2a.
- 6.Determine the zeros (x-intercepts) of the quadratic relation y = x² - 4.
Full range of grade expectations
Solve each problem. Show your work.
- 1.A parabolic archway has a height of 10 meters and a width of 24 meters at its base. The vertex of the parabola is at the highest point of the arch. Write an equation for the parabola in vertex form, assuming the vertex is at (0, 10).
- 2.Factor the quadratic expression: 3x² + 11x - 4.
- 3.Find the vertex, axis of symmetry, and the zeros of the quadratic relation y = x² - 6x + 5.
- 4.A projectile is launched from a height of 2 meters with an initial upward velocity of 20 meters per second. The height 'h' (in meters) of the projectile after 't' seconds is given by the equation h = -4.9t² + 20t + 2. Use the quadratic formula to find the time(s) when the projectile hits the ground (h = 0). Round your answers to two decimal places.
- 5.Compare the two quadratic relations: y = 2(x - 1)² + 3 and y = -x² + 4x - 1. Which parabola opens upwards and which opens downwards? Which one has a vertex with a smaller y-coordinate?
- 6.The path of a water jet from a fountain can be modeled by the equation y = -1/10 x² + 2x, where 'x' is the horizontal distance from the nozzle and 'y' is the vertical height. What is the maximum height the water jet reaches? How far horizontally from the nozzle does this maximum height occur?
Want Unlimited Quadratic Relations Practice?
Sign up for free to unlock AI-generated worksheets, instant grading, and a personalized study plan tailored to your child's level.
Create a Free AccountFrequently Asked Questions
How often should my child practice quadratic relations?
Short daily practice sessions of 10-15 minutes are more effective than long weekly sessions. Consistency builds lasting understanding.
How do I know if my child is at the right level for these worksheets?
If your child can complete about 70% of the problems correctly, the level is appropriate. If it's too easy or too hard, try an adjacent grade level.
Can I use these worksheets for homeschool?
Yes. The worksheets align with standard curriculum expectations and can supplement any math program. Generate multiple worksheets to create a full practice set.