2. Unit 4: Graphing Quadratic Relations
  3. Lesson 2: Graphing and Equations in Vertex Form

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Graphing and Equations in Vertex Form

Source: Chalkboard Equations - marekuliasz/iStock/Getty Images

Graphing a Parabola

Graphing helps us visualize and check our work.

 

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Lesson Goals

  • Describe the transformations that are applied to \(y=x^2\) to obtain the graph of \(y=a(x-h)^2+k\).
  • Sketch the graph of a quadratic relation whose equation is given in the form \(y=a(x-h)^2+k\).
  • Identify the equation of a quadratic relation when given its graph.

Try This

A projectile is launched upward from a roof, reaching a maximum height of \(20\) metres after \(1\) second. The projectile hits the ground \(3\) seconds after being launched.  

The relationship between the height \(h\), in metres and time \(t\), in seconds is quadratic.

  1. Find the equation of this relation.
  2. What is the initial height from which the projectile is launched?