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:

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### 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
Transcribed Image Text:### 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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