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Quadratic Functions in Vertex form

Sep 17, 2022
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Key Concepts

  • Explain the graph of 𝒈(𝒙)=x2+k
  • Explain the graph of 𝒈(𝒙)=(x-h)2
  • Define the vector form of a quadratic function
  • Graph using vertex form of a quadratic function

Vertex form of the quadratic function 

The function f(x) = a(x−h)2+k where a≠0 is called the vertex form of the quadratic function

Vertex form of the quadratic function 
  • The vertex of the graph g is (h, k). 
  • The graph of f(x) = (x−h)2+k is a translation of the function f(x) = x2 that is translated in h units horizontally and kk units vertically. 
  • The value of a does not affect the location of the vertex. 

Graph of g(x) = x2 + k

  • The value of k in g(x) = x2+k translates the graph of parent function f, vertically k units. 
  • The value of k does not affect the axis of symmetry. 
Graph of g(x) = x2 + k

Graph of g(x) = (x−h)2

  • The value of h in g(x) = (x−h)2 translates the graph of parent function f, horizontally h units. 
  • The vertex of the graph g is (0, h). 
Graph of g(x) = (x−h)2
  • The value of h translates the axis of symmetry. 

Graph using vertex form of the quadratic function 

  • Step 1: Plot the vertex and axis of symmetry. 
  • Step 2: Evaluate the function to find other points. 
  • Step 3: Draw the parabola through the points. 

Exercise

1. Identify the vertex and axis of symmetry of graph g(x) = x2+2.

2. Write the function in vertex form.

 Write the function in vertex form.

3. Sketch the graph of f(x) = 0.5(x + 2)2 + 2.

4. Write the function in vertex form.

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 Write the function in vertex form.

5. Identify the vertex and axis of symmetry of graph g(x) = -0.75(X – 5)2 + 6.

Concept Map

  • The function f(x) = a(x−h)2+k where a≠0 is called the vertex form of the quadratic function
  • The vertex of the graph g is (h, k)
  • The graph of f(x) = (x−h)2+k is a translation of the function f(x) = x2 that is translated h units horizontally and k units vertically. 
Concept Map

What have we learned

  • The function f(x) = a(x−h)2+k where a≠0 is called the vertex form of the quadratic function
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