4:37 90 Done deltamath.com Assignment Overview 1 DeltaMath Score: 7/12 Penalty: none Axis of Symmetry and Vertex (with Formula) Question Video Examples Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an \( (x, y) \) point. \[ y=5 x^{2}+20 x+35 \] Answer Attempt 1 out of 3 \( \square \) Submit Answer Copyright ©2025 DeltaMath.com All Rights Reserved. Terms \& Policies

To find the **vertex** of the parabola defined by the equation: \[ y = 5x^{2} + 20x + 35 \] we can use the **vertex formula** for a quadratic function in the form \( y = ax^{2} + bx + c \): \[ x = -\frac{b}{2a} \] Once we have the \( x \)-coordinate of the vertex, we can substitute it back into the original equation to find the corresponding \( y \)-coordinate. ### Step-by-Step Solution 1. **Identify the coefficients** \( a \), \( b \), and \( c \) from the quadratic equation: \[ a = 5,\quad b = 20,\quad c = 35 \] 2. **Find the \( x \)-coordinate of the vertex** using the formula: \[ x = -\frac{b}{2a} = -\frac{20}{2 \times 5} = -\frac{20}{10} = -2 \] 3. **Find the \( y \)-coordinate** by plugging \( x = -2 \) back into the original equation: \[ y = 5(-2)^{2} + 20(-2) + 35 \] \[ y = 5(4) - 40 + 35 \] \[ y = 20 - 40 + 35 \] \[ y = 15 \] 4. **Write the coordinates of the vertex** as an ordered pair: \[ \text{Vertex} = (-2,\ 15) \] ### Final Answer \[ (-2,\ 15) \]