
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Transcribed Image Text:**Graphing Quadratic Functions**
Graph the quadratic function \( y = -x^2 + 2x + 3 \). Analyze its key characteristics, including the vertex and the intercepts.
### Key Elements to Identify:
1. **Vertex:**
- Use the vertex formula \( x = -\frac{b}{2a} \) to find the x-coordinate.
- Calculate \( y \) by substituting \( x \) back into the equation.
2. **Intercepts:**
- **y-intercept:** Set \( x = 0 \) and solve for \( y \).
- **x-intercepts:** Set \( y = 0 \) and solve the quadratic equation for \( x \).
When graphing, remember:
- The graph is a parabola opening downwards because the coefficient of \( x^2 \) is negative.
- Plot the vertex and intercepts accurately to depict the parabola’s shape.
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