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...
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Transformation of Graphs
The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.
Exponential Functions
The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.
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![**Finding the x-intercepts of a Quadratic Function**
**Problem:**
Find the x-intercepts (if any) for the graph of the quadratic function.
\[2) \ f(x) = x^2 + 16x + 47\]
Give your answers in exact form.
---
### Approach to Solve:
To find the x-intercepts of a quadratic function, we need to solve for the values of \( x \) where \( f(x) = 0 \).
For the given quadratic function:
\[ f(x) = x^2 + 16x + 47 \]
1. **Set the quadratic function equal to zero:**
\[ x^2 + 16x + 47 = 0 \]
2. **Solve the quadratic equation:**
Use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \( a = 1 \), \( b = 16 \), and \( c = 47 \).
---
### Explanation of Graphs or Diagrams:
No graphs or diagrams are present in this image. The problem focuses solely on solving the quadratic equation provided.
**Note:** Make sure to explain the steps clearly on your educational website.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77a13500-3283-4aa2-b558-e9fbf21d692d%2F2362f260-9a17-4700-9575-39e2e3123d8f%2F350mgcg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the x-intercepts of a Quadratic Function**
**Problem:**
Find the x-intercepts (if any) for the graph of the quadratic function.
\[2) \ f(x) = x^2 + 16x + 47\]
Give your answers in exact form.
---
### Approach to Solve:
To find the x-intercepts of a quadratic function, we need to solve for the values of \( x \) where \( f(x) = 0 \).
For the given quadratic function:
\[ f(x) = x^2 + 16x + 47 \]
1. **Set the quadratic function equal to zero:**
\[ x^2 + 16x + 47 = 0 \]
2. **Solve the quadratic equation:**
Use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \( a = 1 \), \( b = 16 \), and \( c = 47 \).
---
### Explanation of Graphs or Diagrams:
No graphs or diagrams are present in this image. The problem focuses solely on solving the quadratic equation provided.
**Note:** Make sure to explain the steps clearly on your educational website.
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