### Quadratic Functions: Graphing and Finding the Axis of Symmetry#### 5. Graph the function on scrap paper: $ Y = -2x^2 + 8x + 9 $In this step, you are asked to graph the quadratic function given by the equation $ Y = -2x^2 + 8x + 9 $. Begin by identifying key features such as the vertex, the axis of symmetry, the y-intercept, and potential x-intercepts. Plot these on a coordinate plane and sketch the parabola.#### 5a. Find the Axis of Symmetry.To find the axis of symmetry for a quadratic function in the standard form $ Y = ax^2 + bx + c $, use the formula:\[ x = \frac{-b}{2a} \]For the given function $ Y = -2x^2 + 8x + 9 $:- $a = -2$- $b = 8$Substitute these values into the formula:\[ x = \frac{-8}{2(-2)} = \frac{-8}{-4} = 2 \]#### Axis of Symmetry:\[ x = 2 \]This line $ x = 2 $ is the vertical line that divides the parabola into two symmetrical halves. It passes through the vertex of the parabola.### Note on Graphs and Diagrams:In this document, there is a reference to graphing a quadratic function which involves plotting it on a coordinate plane. While the actual graph is not provided in this text, key steps involve:1. **Identifying the Vertex**: The vertex can be found by substituting $ x = 2 $ back into the original equation to find the corresponding $ Y $ value.2. **Y-Intercept**: The y-intercept is the point where $ x = 0 $, which here evaluates to $ Y = 9 $.3. **Plotting the Points**: Once key points are identified, plotting them on a coordinate graph is the next step to visualize the parabola.Graphing and understanding the axis of symmetry are fundamental skills in studying quadratic functions in algebra.

To graph a quadratic equation, arbitrary points of x are substituted to find the corresponding…

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5. Graph the function on scrap paper: Y= -2x+ 8x+9 5a. Find the Axis of Symmetry. %3D Axis of Symmetry: 2a

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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Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

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### Quadratic Functions: Graphing and Finding the Axis of Symmetry

#### 5. Graph the function on scrap paper: $ Y = -2x^2 + 8x + 9 $

In this step, you are asked to graph the quadratic function given by the equation $ Y = -2x^2 + 8x + 9 $. Begin by identifying key features such as the vertex, the axis of symmetry, the y-intercept, and potential x-intercepts. Plot these on a coordinate plane and sketch the parabola.

#### 5a. Find the Axis of Symmetry.

To find the axis of symmetry for a quadratic function in the standard form $ Y = ax^2 + bx + c $, use the formula:

\[ x = \frac{-b}{2a} \]

For the given function $ Y = -2x^2 + 8x + 9 $:

- $a = -2$
- $b = 8$

Substitute these values into the formula:

\[ x = \frac{-8}{2(-2)} = \frac{-8}{-4} = 2 \]

#### Axis of Symmetry:

\[ x = 2 \]

This line $ x = 2 $ is the vertical line that divides the parabola into two symmetrical halves. It passes through the vertex of the parabola.

### Note on Graphs and Diagrams:
In this document, there is a reference to graphing a quadratic function which involves plotting it on a coordinate plane. While the actual graph is not provided in this text, key steps involve:

1. **Identifying the Vertex**: The vertex can be found by substituting $ x = 2 $ back into the original equation to find the corresponding $ Y $ value.
2. **Y-Intercept**: The y-intercept is the point where $ x = 0 $, which here evaluates to $ Y = 9 $.
3. **Plotting the Points**: Once key points are identified, plotting them on a coordinate graph is the next step to visualize the parabola.

Graphing and understanding the axis of symmetry are fundamental skills in studying quadratic functions in algebra.

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