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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Question
![**Problem Statement:**
Put the equation \( y = -3(x + 2)^2 + 5 \) into general form \( y = ax^2 + bx + c \).
**Solution:**
To convert the given equation into general form, we need to expand it:
1. Start with the equation:
\[
y = -3(x + 2)^2 + 5
\]
2. Expand \( (x + 2)^2 \):
\[
(x + 2)^2 = x^2 + 4x + 4
\]
3. Substitute back into the equation:
\[
y = -3(x^2 + 4x + 4) + 5
\]
4. Distribute the \(-3\):
\[
y = -3x^2 - 12x - 12 + 5
\]
5. Combine like terms:
\[
y = -3x^2 - 12x - 7
\]
The equation in general form is \( y = -3x^2 - 12x - 7 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82675cc8-5905-4df8-bf22-3b83412d0705%2F246dbe58-efbf-42d5-a920-28b383216189%2F4b4xjhs_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Put the equation \( y = -3(x + 2)^2 + 5 \) into general form \( y = ax^2 + bx + c \).
**Solution:**
To convert the given equation into general form, we need to expand it:
1. Start with the equation:
\[
y = -3(x + 2)^2 + 5
\]
2. Expand \( (x + 2)^2 \):
\[
(x + 2)^2 = x^2 + 4x + 4
\]
3. Substitute back into the equation:
\[
y = -3(x^2 + 4x + 4) + 5
\]
4. Distribute the \(-3\):
\[
y = -3x^2 - 12x - 12 + 5
\]
5. Combine like terms:
\[
y = -3x^2 - 12x - 7
\]
The equation in general form is \( y = -3x^2 - 12x - 7 \).
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