## 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) = x^{2}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) = x^{2} + k

- The value of k in g(x) = x
^{2}+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) = x^{2}+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) = x^{2}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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