To complete the square for the quadratic expression x² + 5x – 7, we need to focus on the x² and 5x part. The general process involves finding a constant that makes the expression a perfect square trinomial.
First, we look at the coefficient of the x-term, which is 5. To find the constant term, we take half of this coefficient and square it. Half of 5 is 2.5, and squaring it gives us 6.25.
Now we can write the expression as:
- x² + 5x + 6.25 – 6.25 – 7
This simplifies to:
- (x + 2.5)² – 13.25
Therefore, the constant term needed to complete the square is 6.25. When added to the original expression, we can represent it in vertex form, which provides clearer insights about the graph of the quadratic function.