Attached problem- find the vertex of the parabola with work and write in (x,y) form. **Problem 3: Finding the Vertex of a Parabola**Given the quadratic function \( f(x) = 4x^2 + 40x + 104 \), determine the vertex of the parabola described by this equation. Make sure to write the answer in the correct \((x, y)\) form.*Solution:*To find the vertex of a parabola given by the quadratic equation \( f(x) = ax^2 + bx + c \), we use the vertex formula:\[ x = -\frac{b}{2a} \]1. Identify the coefficients \( a \), \( b \), and \( c \) from the equation: - \( a = 4 \) - \( b = 40 \) - \( c = 104 \)2. Plug the coefficients into the vertex formula to find the x-coordinate of the vertex:\[ x = -\frac{40}{2 \cdot 4} = -\frac{40}{8} = -5 \]3. Substitute \( x = -5 \) back into the original quadratic equation to find the y-coordinate of the vertex:\[ f(-5) = 4(-5)^2 + 40(-5) + 104 \]\[ f(-5) = 4(25) + 40(-5) + 104 \]\[ f(-5) = 100 - 200 + 104 \]\[ f(-5) = 4 \]4. Therefore, the vertex of the parabola is:\[ (-5, 4) \]The vertex in \((x, y)\) form is \( (-5, 4) \).Make sure to refer back to guidelines on solving quadratic equations and the vertex form of parabolas for further practice.

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Answered: 3) Find the vertex of the parabola f(x)…

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3) Find the vertex of the parabola f(x) = 4x² + 40x+104. Write in correct (x, y) form.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Attached problem- find the vertex of the parabola with work and write in (x,y) form.

**Problem 3: Finding the Vertex of a Parabola**

Given the quadratic function \( f(x) = 4x^2 + 40x + 104 \), determine the vertex of the parabola described by this equation. Make sure to write the answer in the correct \((x, y)\) form.

*Solution:*

To find the vertex of a parabola given by the quadratic equation \( f(x) = ax^2 + bx + c \), we use the vertex formula:
\[ x = -\frac{b}{2a} \]

1. Identify the coefficients \( a \), \( b \), and \( c \) from the equation:
- \( a = 4 \)
- \( b = 40 \)
- \( c = 104 \)

2. Plug the coefficients into the vertex formula to find the x-coordinate of the vertex:
\[ x = -\frac{40}{2 \cdot 4} = -\frac{40}{8} = -5 \]

3. Substitute \( x = -5 \) back into the original quadratic equation to find the y-coordinate of the vertex:
\[ f(-5) = 4(-5)^2 + 40(-5) + 104 \]
\[ f(-5) = 4(25) + 40(-5) + 104 \]
\[ f(-5) = 100 - 200 + 104 \]
\[ f(-5) = 4 \]

4. Therefore, the vertex of the parabola is:
\[ (-5, 4) \]

The vertex in \((x, y)\) form is \( (-5, 4) \).

Make sure to refer back to guidelines on solving quadratic equations and the vertex form of parabolas for further practice.

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