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Not so long ago, you learned in this course that the vertex of the parabola y = ax? + b bx + c occurs at x = 2a - You remember that, right? Use calculus to prove this fact. Hint: What should the slope of the tangent line be at the vertex? vertex X-axis -1- vertex -2 10 X-axis y-axis to SIxe-A

Not so long ago, you learned in this course that the vertex of the parabola y = ax? + b bx + c occurs at x = 2a - You remember that, right? Use calculus to prove this fact. Hint: What should the slope of the tangent line be at the vertex? vertex X-axis -1- vertex -2 10 X-axis y-axis to SIxe-A

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...
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**Transcription:** 4. Not so long ago, you learned in this course that the vertex of the parabola \( y = ax^2 + bx + c \) occurs at \( x = -\frac{b}{2a} \). You remember that, right? Use calculus to prove this fact. Hint: What should the slope of the tangent line be at the vertex? **Explanation of Graphs:** - **Left Graph:** - The graph depicts a parabola opening upwards. - The vertex of the parabola is marked with a pink dot and labeled "vertex" on the x-axis. - The axes are labeled as "x-axis" and "y-axis" indicating the horizontal and vertical directions, respectively. - The vertex is located at a negative value on the x-axis. - **Right Graph:** - The graph shows a parabola opening downwards. - The vertex is indicated by a pink dot and labeled "vertex" on the x-axis. - Similar to the left graph, the axes are labeled as "x-axis" and "y-axis." - The vertex is positioned at a positive value on the x-axis. Both graphs illustrate the concept of the parabola having a vertex where the slope of the tangent line is zero.
Transcribed Image Text:**Transcription:** 4. Not so long ago, you learned in this course that the vertex of the parabola \( y = ax^2 + bx + c \) occurs at \( x = -\frac{b}{2a} \). You remember that, right? Use calculus to prove this fact. Hint: What should the slope of the tangent line be at the vertex? **Explanation of Graphs:** - **Left Graph:** - The graph depicts a parabola opening upwards. - The vertex of the parabola is marked with a pink dot and labeled "vertex" on the x-axis. - The axes are labeled as "x-axis" and "y-axis" indicating the horizontal and vertical directions, respectively. - The vertex is located at a negative value on the x-axis. - **Right Graph:** - The graph shows a parabola opening downwards. - The vertex is indicated by a pink dot and labeled "vertex" on the x-axis. - Similar to the left graph, the axes are labeled as "x-axis" and "y-axis." - The vertex is positioned at a positive value on the x-axis. Both graphs illustrate the concept of the parabola having a vertex where the slope of the tangent line is zero.
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