### Graphing Parabolas**Graph the parabola:**\[ y = -3x^2 + 30x - 70 \]**Instructions:**- Plot five points on the parabola: - The **vertex**. - Two points to the left of the vertex. - Two points to the right of the vertex.**Process:**1. **Find the Vertex**: The x-coordinate of the vertex for a parabola given by \( y = ax^2 + bx + c \) can be found using the formula: \[ x = -\frac{b}{2a} \] Plug in the values from the equation \( y = -3x^2 + 30x - 70 \). - \( a = -3 \) - \( b = 30 \) \[ x = -\frac{30}{2(-3)} = \frac{30}{6} = 5 \] Now, find the y-coordinate by substituting \( x = 5 \) back into the parabola equation. \[ y = -3(5)^2 + 30(5) - 70 \] \[ y = -3(25) + 150 - 70 \] \[ y = -75 + 150 - 70 = 5 \] So, the vertex is (5, 5).2. **Plot Additional Points**: - Select points to the left and right of \( x = 5 \), for example, \( x = 3, 4 \) and \( x = 6, 7 \). - Calculate the corresponding y-values for these x-values by plugging them into the parabola equation.3. **Graph Points**: - Mark the points on the graph with the calculated coordinates.**Graph Explanation:**- The graph provided displays an interactive plotting interface.- There are several tools available: - **Pencil Tool**: Allows drawing or marking points on the graph. - **Eraser Tool**: Erases markings or plots on the graph. - **Grid Tool**: Shows or hides the grid. - **Curve Tool**: Draws curves or to connect plotted points smoothly.**Interactive Tools:**- **Explanation Button**: Provides a detailed

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Graph the parabola. y=-3x²+30x-70 Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-funct button. Vy X ? -12 -10 12- 10+ 18+

Graph the parabola. y=-3x²+30x-70 Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-funct button. Vy X ? -12 -10 12- 10+ 18+

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

### Graphing Parabolas

**Graph the parabola:**

\[ y = -3x^2 + 30x - 70 \]

**Instructions:**

- Plot five points on the parabola:
- The **vertex**.
- Two points to the left of the vertex.
- Two points to the right of the vertex.

**Process:**

1. **Find the Vertex**:
The x-coordinate of the vertex for a parabola given by \( y = ax^2 + bx + c \) can be found using the formula:
\[ x = -\frac{b}{2a} \]
Plug in the values from the equation \( y = -3x^2 + 30x - 70 \).
- \( a = -3 \)
- \( b = 30 \)

\[
x = -\frac{30}{2(-3)} = \frac{30}{6} = 5
\]

Now, find the y-coordinate by substituting \( x = 5 \) back into the parabola equation.
\[
y = -3(5)^2 + 30(5) - 70
\]
\[
y = -3(25) + 150 - 70
\]
\[
y = -75 + 150 - 70 = 5
\]

So, the vertex is (5, 5).

2. **Plot Additional Points**:
- Select points to the left and right of \( x = 5 \), for example, \( x = 3, 4 \) and \( x = 6, 7 \).
- Calculate the corresponding y-values for these x-values by plugging them into the parabola equation.

3. **Graph Points**:
- Mark the points on the graph with the calculated coordinates.

**Graph Explanation:**

- The graph provided displays an interactive plotting interface.
- There are several tools available:
- **Pencil Tool**: Allows drawing or marking points on the graph.
- **Eraser Tool**: Erases markings or plots on the graph.
- **Grid Tool**: Shows or hides the grid.
- **Curve Tool**: Draws curves or to connect plotted points smoothly.

**Interactive Tools:**

- **Explanation Button**: Provides a detailed

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