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Grade 10 Algebra Worksheet: Quadratic Functions and Transformations

Worksheet
Grade 8
English

Grade 10 Algebra Worksheet: Quadratic Functions and Transformations

Graph Interpretation Questions

Instructions: For each question, refer to the provided coordinate grid and answer the questions below. Leave space to show your working and explain your reasoning.
  1. The graph of a quadratic function is shown below.

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a) Write the equation of the parabola in vertex form.
b) What is the axis of symmetry of the parabola?
  1. The graph below shows a parabola opening downwards with vertex at (-1, 4) and y-intercept at (0, 3).

a) Write the equation of the parabola in standard form.
b) What are the coordinates of the vertex?
  1. Examine the graph below. The parabola passes through the points (1, 0), (3, 0), and its vertex is at (2, -4).

a) Write the equation of the parabola in factored form.
b) What is the minimum value of the function?


Vertex Form and Standard Form Conversion

Instructions: Convert between vertex form and standard form as required. Leave space for your calculations.
  1. Write the quadratic equation
    
    in standard form.
  1. Convert the following equation to vertex form:
    
  1. Given
    
    , expand and write the equation in standard form.


Real-World Applications: Projectile Motion

Instructions: Solve the following word problems. Show all your calculations and state your answers clearly.
  1. A ball is thrown upward from ground level with a velocity such that its height (in meters) after
    
    seconds is given by
    
    .
a) What is the maximum height reached by the ball?
b) After how many seconds does the ball return to the ground?
  1. A diver jumps from a platform 10 meters above the water. Her height (in meters)
    
    seconds after jumping is
    
    .
a) What is the maximum height reached by the diver?
b) After how many seconds does she hit the water?


Challenge: Quadratic Transformations

Instructions: For each question, describe or determine the transformed equation. Show all your steps and reasoning.
  1. The graph of
    
    is reflected over the x-axis, vertically stretched by a factor of 2, and shifted right by 3 units. Write the equation of the transformed function.
  1. Starting with
    
    , the graph is compressed vertically by a factor of
    
    and shifted down by 4 units. What is the equation of the new function?

Space for Student Working:
Leave sufficient space under each question for students to show their calculations and explanations.

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