6. Find the axis of symmetry and the \( y \)-intercept \( f \) a. \( y=2 x^{2}+8 x-5 \)

To analyze the quadratic function \( y = 2x^{2} + 8x - 5 \), we'll determine both the **axis of symmetry** and the **\( y \)-intercept**. ### 1. Axis of Symmetry For any quadratic function in the form \( y = ax^{2} + bx + c \), the **axis of symmetry** can be found using the formula: \[ x = -\frac{b}{2a} \] **Given:** - \( a = 2 \) - \( b = 8 \) **Calculation:** \[ x = -\frac{8}{2 \times 2} = -\frac{8}{4} = -2 \] **Result:** - **Axis of Symmetry:** \( x = -2 \) ### 2. \( y \)-Intercept The **\( y \)-intercept** occurs where the graph crosses the \( y \)-axis. At this point, the value of \( x \) is **0**. **To find the \( y \)-intercept:** - Substitute \( x = 0 \) into the original equation. \[ y = 2(0)^{2} + 8(0) - 5 = 0 + 0 - 5 = -5 \] **Result:** - **\( y \)-Intercept:** \( (0, -5) \) or simply \( y = -5 \) ### Summary - **Axis of Symmetry:** \( x = -2 \) - **\( y \)-Intercept:** \( (0, -5) \) These properties provide valuable information about the symmetry and position of the quadratic graph on the coordinate plane.