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.

Answered: Image /qna-images/answer/ab59f21f-4043-4380-b365-8e83fd957ac6.jpg

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

Math

Algebra

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,...

See similar textbooks

Related questions

Q: Find x-intercepts of the parabola y= -2x² + 3x + 3 (Round your answers to two decimal places.) Write…

A: Given: y=-2x2+3x+3 As we know that: To calculate the x-intercept, we need to solve for x after…

Q: Today's Date: 2,4) ( y- 4 )² = 20 ( x+ 2 )*) カ=人 Describe in as much detail as possible how you…

Q: The vertex of the parabola with focus (-2,-4) and directrix y - 4 is o (1,-4) 0 (-2,1) O (0,-4) O…

A: Given,drectrix of parabola is y=4,And focus is at (-2,-4)It is clear that parabola is open down,and…

Q: 8) and directrix y = 7? A B y = -(x - 5)² +8 - y=- 1 -(x + 5)² +8 y = -(x + 5)² - 8 D_y==(x + 5)² +8…

A: Given query is to find the equation of the parabola.

Q: What is the equation of a parabola in standard form with vertex V(3, – 3) and focus F(3, 2)? A (x-…

A: NOTE: Refresh your page if you can't see any equations. . the vertex is at and the focus is at

Q: create a unique parabola for the pattern fx=(x-a)(x-b), integers cannot be one or zero for a and b…

A: We have to create a unique parabola for the pattern f(x)=(x-a)(x-b).

Q: Find the equation of the parabola with vertex at (2,-1), axis is parallel to the y-axis and passing…

A: Equation of parabola parallel to y axis is given by as: (x-h)²= 4a(y-k)

Q: (V5V5)3

Q: What is the equation of the parabola with axis parallel to the x-axis, whose vertex is at (-1,7) and…

Q: Which point is the vertex of the parabola y = 6(x+3)^2 - 5?

Q: Find the equation of the following parabola. Express your answer in standard form. 20 -15 -10 -5 15…

A: The standard equation of the parabola is written in the form ofy=ax2+bx+c

Q: Find an equation for the hyperbola whose transverse axis is horizontal, with center at (1, -5) and…

A: Given problem:- Find an equation for the hyperbola whose transverse axis is horizontal, with center…

Q: The standard form of the equation of the parabola with vertex (-2, 5) and point (0, 9) is: = (x +…

Q: Find the standard form of a parabola with the following properties: Center at the origin…

Q: Find the standard equation of the hyperbola that satisfies the conditions Center (0 ,5), one corner…

A: The equation of hyperbola with center ( h , k ) and the conjugate axis, vertical is as follows.…

Q: 3) Explain how changing the a, h, and k variables affect the shape of the parabola in the vertex…

A: The vertex form of a parabola is given by y = a(x - h)² + k. In this equation, (h, k) is the vertex…

Q: Write the equation for a parabola that opens sideways, whose vertex is at (0, 2), and that passes…

A: We are required to: Write the equation of the parabola that open sideways whose vertex is at (0,2)…

Q: The vertex of. through (6, 15) is (4,11). find "all for the standard form of this parabola, line…

Q: What is the equation for a parabola

Q: Hate 4 The parabolas x=y² and X=2y_y² ? [ans: 1

A: The parabola equations :x=y2x=2y-y2

Q: Find an equation for the set of all possible vertex points of a parabola that has an x-intercept at…

A: Consider that the origin (0, 0) is shifted to a point (h, k). Thus, any point (x, y) will be shifted…

Q: y=-2(x + 5)² y = -2(x - 5)² y = 2(x - 5)² is the equation of the parabola with vertex (0,4) and…

A: Topic:- geometry and parabola

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

How do you know which standard form equation to put a parabola into when you are given information about the parabola and asked to put it into standard form?
3
6) Find the equation of a parabola containing points any method: 16), (-3, -0.5), (0, -5) (-6,
Write the equation of the hyperbola in standard form ((x-h)/a)^2 - ((y-k)/b)^2 =1