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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![### 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8175d67d-08a3-43eb-bfb3-8ec86236d575%2F900d57a7-e9e5-4148-9a63-868bae5a5f3a%2F3q4fo02_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### 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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