### Understanding the Quadratic FunctionConsider the function: $ f(x) = 2x^2 + 24x + 40 $#### 1. Y-InterceptThe y-intercept is the point where the graph of the function crosses the y-axis. This occurs when $ x = 0 $.The y-intercept is at $ y = $ [Text Box]#### 2. X-InterceptsThe x-intercepts are the points where the graph of the function crosses the x-axis. These can be found by setting the function $ f(x) $ to zero and solving for $ x $.The x-intercepts are at $ x = $ [Text Box](Enter solutions separated by a comma)#### 3. VertexThe vertex of a quadratic function in the form of $ ax^2 + bx + c $ can be found using the formula:\[ x_{vertex} = -\frac{b}{2a} \]Substitute the value of $ x_{vertex} $ into the function to find the y-coordinate of the vertex.The vertex is at the point [Text Box](Give your answer as an ordered pair)#### 4. Direction of the GraphThe direction of a parabolic graph of a quadratic function $ ax^2 + bx + c $ is determined by the coefficient $ a $:- If $ a > 0 $, the parabola opens upwards.- If $ a < 0 $, the parabola opens downwards.The direction of the graph is like which of the following:[Diagram Section]- The left diagram shows a parabola opening upwards.- The right diagram shows a parabola opening downwards.Choose the correct direction:[Radio Button] Upwards [Radio Button] Downwards

Answered: Image /qna-images/answer/488bbfd7-290d-49bd-9c02-dbd9cf74d7c2.jpg

Consider the function: f(x) 2x2 + 24x + 40 The y-intercept is at y = The x-intercepts are at x = (Enter solutions separated by a comma) The vertex is at the point (Give your answer as an ordered pair) The direction of the graph is like which of the following:

Consider the function: f(x) 2x2 + 24x + 40 The y-intercept is at y = The x-intercepts are at x = (Enter solutions separated by a comma) The vertex is at the point (Give your answer as an ordered pair) The direction of the graph is like which of the following:

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Understanding the Quadratic Function

Consider the function: $ f(x) = 2x^2 + 24x + 40 $

#### 1. Y-Intercept
The y-intercept is the point where the graph of the function crosses the y-axis. This occurs when $ x = 0 $.

The y-intercept is at $ y = $ [Text Box]

#### 2. X-Intercepts
The x-intercepts are the points where the graph of the function crosses the x-axis. These can be found by setting the function $ f(x) $ to zero and solving for $ x $.

The x-intercepts are at $ x = $ [Text Box]
(Enter solutions separated by a comma)

#### 3. Vertex
The vertex of a quadratic function in the form of $ ax^2 + bx + c $ can be found using the formula:

\[ x_{vertex} = -\frac{b}{2a} \]

Substitute the value of $ x_{vertex} $ into the function to find the y-coordinate of the vertex.
The vertex is at the point [Text Box]
(Give your answer as an ordered pair)

#### 4. Direction of the Graph
The direction of a parabolic graph of a quadratic function $ ax^2 + bx + c $ is determined by the coefficient $ a $:
- If $ a > 0 $, the parabola opens upwards.
- If $ a < 0 $, the parabola opens downwards.

The direction of the graph is like which of the following:

[Diagram Section]
- The left diagram shows a parabola opening upwards.
- The right diagram shows a parabola opening downwards.

Choose the correct direction:
[Radio Button] Upwards
[Radio Button] Downwards

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