Question
The graph of f(x)=x2 is shown.
Use the parabola tool to graph the function g(x)=(12x)2.
To graph a parabola, first plot the vertex, and then plot another point on the parabola.
Use the parabola tool to graph the function g(x)=(12x)2.
To graph a parabola, first plot the vertex, and then plot another point on the parabola.
Answers
GPT-4o mini
To graph the function \( g(x) = (12x)^2 \), we first need to identify the vertex and then plot another point.
1. **Vertex**:
The function \( g(x) = (12x)^2 \) is a quadratic function in the form of \( y = ax^2 \), where \( a = 144 \). Since this function has no linear term or constant term, the vertex of the parabola is at the origin \( (0, 0) \).
2. **Plotting another point**:
We can choose an x-value to find another point on the graph. Let's pick \( x = 1 \):
\[
g(1) = (12 \cdot 1)^2 = 12^2 = 144
\]
Therefore, the point \( (1, 144) \) is also on the graph of \( g(x) \).
3. **Graph**:
You should now plot the points \( (0, 0) \) and \( (1, 144) \). Since this parabola opens upwards (as the coefficient of \( x^2 \) is positive), you can draw a symmetric curve around the y-axis.
To summarize:
- The vertex of \( g(x) \) is at \( (0, 0) \).
- A point on the parabola is \( (1, 144) \).
You can continue to find additional points if needed or reflect points across the y-axis for further accuracy. For example, if \( x = -1 \):
\[
g(-1) = (12 \cdot -1)^2 = 144, \quad \text{which gives the point } (-1, 144).
\]
You can plot those points and create the symmetric shape of the parabola.
1. **Vertex**:
The function \( g(x) = (12x)^2 \) is a quadratic function in the form of \( y = ax^2 \), where \( a = 144 \). Since this function has no linear term or constant term, the vertex of the parabola is at the origin \( (0, 0) \).
2. **Plotting another point**:
We can choose an x-value to find another point on the graph. Let's pick \( x = 1 \):
\[
g(1) = (12 \cdot 1)^2 = 12^2 = 144
\]
Therefore, the point \( (1, 144) \) is also on the graph of \( g(x) \).
3. **Graph**:
You should now plot the points \( (0, 0) \) and \( (1, 144) \). Since this parabola opens upwards (as the coefficient of \( x^2 \) is positive), you can draw a symmetric curve around the y-axis.
To summarize:
- The vertex of \( g(x) \) is at \( (0, 0) \).
- A point on the parabola is \( (1, 144) \).
You can continue to find additional points if needed or reflect points across the y-axis for further accuracy. For example, if \( x = -1 \):
\[
g(-1) = (12 \cdot -1)^2 = 144, \quad \text{which gives the point } (-1, 144).
\]
You can plot those points and create the symmetric shape of the parabola.