14) For the function: g(x) = 3x2 -30x+78 %3D A) Convert to standard (vertex) form. gox) = 3( x"-1ox ) + | lox ) +| B) Identify the vertex: C) Identify the axis of symmetry: D) Find the intercepts:
14) For the function: g(x) = 3x2 -30x+78 %3D A) Convert to standard (vertex) form. gox) = 3( x"-1ox ) + | lox ) +| B) Identify the vertex: C) Identify the axis of symmetry: D) Find the intercepts:
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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![### Problem 14
**Given Function**:
\[ g(x) = 3x^2 - 30x + 78 \]
---
**A) Convert to standard (vertex) form.**
Given:
\[ g(x) = 3(x^2 - 10x + 1) \]
---
**B) Identify the vertex:**
To identify the vertex of the quadratic function in standard form, complete the square in the expression inside the parentheses.
---
**C) Identify the axis of symmetry:**
The axis of symmetry can be found using the formula:
\[ x = -\frac{b}{2a} \]
---
**D) Find the intercepts:**
To find the intercepts, set \( g(x) = 0 \) for x-intercepts and set \( x = 0 \) to find the y-intercept.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac7f0f6e-6d20-42e1-81bb-7961a6d3ee59%2F3d4a12e4-a9dd-4ea7-b4fb-2de6fe55aeea%2Fotyskfo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 14
**Given Function**:
\[ g(x) = 3x^2 - 30x + 78 \]
---
**A) Convert to standard (vertex) form.**
Given:
\[ g(x) = 3(x^2 - 10x + 1) \]
---
**B) Identify the vertex:**
To identify the vertex of the quadratic function in standard form, complete the square in the expression inside the parentheses.
---
**C) Identify the axis of symmetry:**
The axis of symmetry can be found using the formula:
\[ x = -\frac{b}{2a} \]
---
**D) Find the intercepts:**
To find the intercepts, set \( g(x) = 0 \) for x-intercepts and set \( x = 0 \) to find the y-intercept.
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