Question
Which equation best matches the graph shown below?
x
y
Answer
Multiple Choice Answers
y, equals, minus, 0, point, 4, left parenthesis, x, minus, 1, right parenthesis, squared, plus, 6y=−0.4(x−1)
2
+6
y, equals, minus, 0, point, 4, left parenthesis, x, plus, 1, right parenthesis, squared, minus, 6y=−0.4(x+1)
2
−6
y, equals, minus, 0, point, 4, left parenthesis, x, minus, 1, right parenthesis, squared, minus, 6y=−0.4(x−1)
2
−6
y, equals, minus, 0, point, 4, left parenthesis, x, plus, 1, right parenthesis, squared, plus, 6y=−0.4(x+1)
2
+6
x
y
Answer
Multiple Choice Answers
y, equals, minus, 0, point, 4, left parenthesis, x, minus, 1, right parenthesis, squared, plus, 6y=−0.4(x−1)
2
+6
y, equals, minus, 0, point, 4, left parenthesis, x, plus, 1, right parenthesis, squared, minus, 6y=−0.4(x+1)
2
−6
y, equals, minus, 0, point, 4, left parenthesis, x, minus, 1, right parenthesis, squared, minus, 6y=−0.4(x−1)
2
−6
y, equals, minus, 0, point, 4, left parenthesis, x, plus, 1, right parenthesis, squared, plus, 6y=−0.4(x+1)
2
+6
Answers
GPT-4o mini
To determine which equation best matches the given graph, we need to analyze the characteristics of each equation and how they relate to the transformations of a standard parabola.
The general form for a parabola that opens downwards is:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola and \(a\) dictates the direction and width (if \(|a| > 1\), it is narrower, if \(|a| < 1\), it is wider) of the parabola.
From the choices provided:
1. **\(y = -0.4(x - 1)^2 + 6\)**: Vertex at (1, 6)
2. **\(y = -0.4(x + 1)^2 - 6\)**: Vertex at (-1, -6)
3. **\(y = -0.4(x - 1)^2 - 6\)**: Vertex at (1, -6)
4. **\(y = -0.4(x + 1)^2 + 6\)**: Vertex at (-1, 6)
To determine which equation matches the graph, the following should be considered:
- The orientation of the parabola (upward or downward).
- The location of the vertex (where the peak or trough of the parabola is located).
- The y-intercept and general shape relative to other points.
If the graph opens downward and has a vertex at (1, 6), then the first equation \(y = -0.4(x - 1)^2 + 6\) would be a correct choice.
If the graph opens downward and has a vertex at (1, -6), the third equation \(y = -0.4(x - 1)^2 - 6\) would fit.
If the graph opens downward and has a vertex at (-1, 6), the fourth would be correct.
If the graph opens downward and has a vertex at (-1, -6), the second would fit.
Since I can't see the graph you're referring to, please compare the characteristics of the graph (especially the vertex and orientation) with those of the options above to determine which equation fits best.
The general form for a parabola that opens downwards is:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola and \(a\) dictates the direction and width (if \(|a| > 1\), it is narrower, if \(|a| < 1\), it is wider) of the parabola.
From the choices provided:
1. **\(y = -0.4(x - 1)^2 + 6\)**: Vertex at (1, 6)
2. **\(y = -0.4(x + 1)^2 - 6\)**: Vertex at (-1, -6)
3. **\(y = -0.4(x - 1)^2 - 6\)**: Vertex at (1, -6)
4. **\(y = -0.4(x + 1)^2 + 6\)**: Vertex at (-1, 6)
To determine which equation matches the graph, the following should be considered:
- The orientation of the parabola (upward or downward).
- The location of the vertex (where the peak or trough of the parabola is located).
- The y-intercept and general shape relative to other points.
If the graph opens downward and has a vertex at (1, 6), then the first equation \(y = -0.4(x - 1)^2 + 6\) would be a correct choice.
If the graph opens downward and has a vertex at (1, -6), the third equation \(y = -0.4(x - 1)^2 - 6\) would fit.
If the graph opens downward and has a vertex at (-1, 6), the fourth would be correct.
If the graph opens downward and has a vertex at (-1, -6), the second would fit.
Since I can't see the graph you're referring to, please compare the characteristics of the graph (especially the vertex and orientation) with those of the options above to determine which equation fits best.