Quadratic Functions in Vertex form
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.
- 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) = (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).
- 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.
3. Sketch the graph of f(x) = 0.5(x + 2)2 + 2.
4. 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.
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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