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.
Practice Worksheet
Grade 10 Quadratic Relations Practice
Solve each problem. Show your work.
- 1.Find the zeros of x² - 2x - 3 = 0: _____
- 2.State the vertex and axis of symmetry of y = 2(x - 2)² - 2: _____
- 3.A ball's height is h(t) = -5(t - 3)² + 20. State its maximum height and when it occurs: _____
- 4.Find the zeros of x² - 4 = 0: _____
- 5.State the vertex and axis of symmetry of y = 2(x - 3)² - 3: _____
- 6.A ball's height is h(t) = -5(t - 4)² + 25. State its maximum height and when it occurs: _____
Show answer key
- Question 1: x = -1, 3
- Question 2: vertex (2, -2); axis x = 2
- Question 3: 20 m at 3 s
- Question 4: x = -2, 2
- Question 5: vertex (3, -3); axis x = 3
- Question 6: 25 m at 4 s
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.Factor the trinomial x² + 7x + 10.
- 2.Identify the vertex (h, k) of the parabola y = (x - 3)² + 5.
- 3.Complete the square for the expression x² + 6x to write it in the form (x + h)² + k.
- 4.Use the quadratic formula to find the roots of x² - 5x + 6 = 0.
- 5.Factor the trinomial x² - 2x - 8.
- 6.State the axis of symmetry for the parabola y = 2(x + 4)² - 1.
Full range of grade expectations
Solve each problem. Show your work.
- 1.Factor the trinomial completely: x² + 7x + 12.
- 2.Convert the quadratic relation y = x² - 6x + 11 into vertex form y = a(x - h)² + k by completing the square.
- 3.Use the quadratic formula to find the roots of the equation 2x² - 5x - 3 = 0.
- 4.Identify the vertex, the axis of symmetry, and the direction of opening for the parabola defined by y = -2(x + 3)² + 5.
- 5.A ball is thrown into the air. Its height in meters is given by h(t) = -5t² + 20t + 1, where t is time in seconds. Determine the maximum height reached by the ball.
- 6.A rectangular garden has a length that is 3 meters more than its width. The area of the garden is 40 square meters. Set up a quadratic equation and solve for the dimensions of the garden.
Practise specific Quadratic Relations skills
Skill map
How quadratic relations skills connect
Shore up what feeds in, work through the core skills in order, then move on to what they unlock. A means the skill has an instant answer checker.
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Core skills — in order
What Your Child Will Learn
Quadratic relations introduce students to their first non-linear function family, and the unit is built around three equivalent ways of seeing the same parabola: factored form, standard form, and vertex form. Students learn to factor trinomials (including cases with a leading coefficient other than 1), expand and simplify to move between forms, and complete the square to convert standard form into vertex form.
From each form, students extract different information efficiently — factored form reveals the zeros, vertex form reveals the maximum or minimum point, and standard form reveals the y-intercept — and they learn to choose the most useful form for a given question. The quadratic formula is introduced for cases that don't factor nicely, along with the discriminant as a quick way to determine how many real roots exist before solving.
Applications include projectile motion, revenue and profit maximization, and area problems, all of which ask students to build a quadratic model from a word problem and then interpret the vertex or zeros in context. This unit is often considered the conceptual core of Grade 10 math, since transformations, factoring fluency, and multiple-representation thinking all resurface in Grade 11 functions.
Skills Covered
- Factoring trinomials, including cases with leading coefficients other than 1
- Converting between standard, factored, and vertex form
- Completing the square to find the vertex
- Using the quadratic formula and discriminant
- Graphing parabolas using transformations of y = x²
- Solving word problems involving maximum, minimum, and zeros
Curriculum Aligned: Core strand of Grade 10 math (MPM2D Principles of Mathematics, with a parallel applied treatment in MFM2P), focused on quadratic functions and their multiple representations.
Parent Tip: If you can't check the factoring by hand, you can still check the final answer — plug the student's roots or vertex back into the original equation with a calculator and see if it works out. Asking 'how do you know this is right?' pushes them toward self-checking habits that matter more than getting confirmation from you.
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.
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Check my workFrequently 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.