| Exam Board | AQA |
|---|
| Module | C1 (Core Mathematics 1) |
|---|
| Year | 2006 |
|---|
| Session | June |
|---|
| Topic | Quadratic Functions |
|---|
2
- Express \(x ^ { 2 } + 8 x + 19\) in the form \(( x + p ) ^ { 2 } + q\), where \(p\) and \(q\) are integers.
- Hence, or otherwise, show that the equation \(x ^ { 2 } + 8 x + 19 = 0\) has no real solutions.
- Sketch the graph of \(y = x ^ { 2 } + 8 x + 19\), stating the coordinates of the minimum point and the point where the graph crosses the \(y\)-axis.
- Describe geometrically the transformation that maps the graph of \(y = x ^ { 2 }\) onto the graph of \(y = x ^ { 2 } + 8 x + 19\).