Homework Help is Here – Start Your Trial Now!
Math
Calculus
Find the general form of the quadratic function that has a vertex of (-4,-1) and a point on the graph (5, 80). f(x) = help (formulas)

Find the general form of the quadratic function that has a vertex of (-4,-1) and a point on the graph (5, 80). f(x) = help (formulas)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
**Problem Statement:** Find the general form of the quadratic function that has a vertex of \((-4, -1)\) and a point on the graph \((5, 80)\). **Equation Form:** \( f(x) = \quad\text{[Input box]}\quad \) help (formulas) **Instructions:** To find the general form of the quadratic function, start by using the vertex form of a quadratic equation, which is: \[ f(x) = a(x - h)^2 + k \] where \( (h, k) \) is the vertex of the parabola. Given: - Vertex: \((-4, -1)\) - Point: \((5, 80)\) **Steps:** 1. Substitute the vertex into the vertex form equation: \[ f(x) = a(x + 4)^2 - 1 \] 2. Use the given point \((5, 80)\) to find the value of \(a\): \[ 80 = a(5 + 4)^2 - 1 \] \[ 80 = a(9)^2 - 1 \] \[ 80 = 81a - 1 \] \[ 81 = 81a \] \[ a = 1 \] 3. Substitute \( a = 1 \) into the equation: \[ f(x) = (x + 4)^2 - 1 \] 4. Expand to find the general form: \[ f(x) = x^2 + 8x + 16 - 1 \] \[ f(x) = x^2 + 8x + 15 \] **Conclusion:** The general form of the quadratic function is: \[ f(x) = x^2 + 8x + 15 \]
Transcribed Image Text:**Problem Statement:** Find the general form of the quadratic function that has a vertex of \((-4, -1)\) and a point on the graph \((5, 80)\). **Equation Form:** \( f(x) = \quad\text{[Input box]}\quad \) help (formulas) **Instructions:** To find the general form of the quadratic function, start by using the vertex form of a quadratic equation, which is: \[ f(x) = a(x - h)^2 + k \] where \( (h, k) \) is the vertex of the parabola. Given: - Vertex: \((-4, -1)\) - Point: \((5, 80)\) **Steps:** 1. Substitute the vertex into the vertex form equation: \[ f(x) = a(x + 4)^2 - 1 \] 2. Use the given point \((5, 80)\) to find the value of \(a\): \[ 80 = a(5 + 4)^2 - 1 \] \[ 80 = a(9)^2 - 1 \] \[ 80 = 81a - 1 \] \[ 81 = 81a \] \[ a = 1 \] 3. Substitute \( a = 1 \) into the equation: \[ f(x) = (x + 4)^2 - 1 \] 4. Expand to find the general form: \[ f(x) = x^2 + 8x + 16 - 1 \] \[ f(x) = x^2 + 8x + 15 \] **Conclusion:** The general form of the quadratic function is: \[ f(x) = x^2 + 8x + 15 \]
Expert Solution
Step 1

Equation of quadratic function having vertex (-4,-1)

 

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS