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# 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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