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Axis of Symmetry and Vertex (with Formula)

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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an point.

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Ask by Huang Erickson. in the United States

Jan 23,2025

Question

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 point.

Answer
Attempt 1 out of 3

Submit Answer
Copyright ©2025 DeltaMath.com All Rights Reserved.
Terms & Policies

Ask by Huang Erickson. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

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

$$
(-2,\ 15)
$$
The vertex of the parabola $$ y = 5x^{2} + 20x + 35 $$ is at the point $$ (-2, 15) $$.

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