Year 9 Maths • AC9M9A04 • Authored homework
Quadratic patterns, graphs and equations
Recognise quadratic patterns, connect tables and graphs, expand or factorise simple quadratics, and solve quadratic equations by suitable methods. Show working, use correct notation and check reasonableness.
Part A
Short-answer questions
Complete the table for y = x^2 when x = -2, -1, 0, 1, 2.
State the shape of the graph of a quadratic relation.
Find the y-intercept of y = x^2 + 3x - 4.
Factorise x^2 + 5x + 6.
Solve x^2 = 49.
Find the axis of symmetry of y = x^2.
Explain how first differences and second differences help identify a quadratic pattern.
Expand (x + 4)(x - 2).
Correct this error: x^2 + 9 = (x + 3)^2.
Give one real-world situation that can form a quadratic relationship.
Part B
Long-answer questions
Use a table of values to sketch y = x^2 - 4, then describe the vertex and intercepts.
Factorise and solve x^2 + 7x + 12 = 0. Check both solutions by substitution.
Compare the graphs of y = x^2 and y = x^2 + 5. Explain what changes and what stays the same.
A ball is thrown and its height is modelled by h = -t^2 + 6t. Find when it is on the ground and interpret the answer.
Use second differences to decide whether a sequence is quadratic, then predict the next two terms.
Expand (2x + 1)(x - 3), then explain how the expanded form connects to graphing.
Create a quadratic equation with two integer solutions, then expand it and solve it again.
Explain why a quadratic graph can have zero, one or two x-intercepts.
Solve a practical area problem that leads to a quadratic expression.
Write a full response connecting a quadratic table, graph, equation, vertex and intercepts.
Part C
Research and understanding task
Find or design a real situation that can be modelled by a quadratic, such as projectile motion, area, braking distance or a parabolic shape. Create a simple model, table and explanation.