which quadratic rule represents the data in the table
1. y = -2x2 + 5
2. y= -x2 + 5
3.y= x2 - 5
4. y= x2 + 5
explain why
Without a table of data provided, it is impossible to determine which quadratic rule represents the data. Please provide the table of data.
To determine which quadratic rule represents the data in the table, we need to look at the coefficients and the shape of the graph.
1. The quadratic rule y = -2x^2 + 5 has a negative coefficient (-2) in front of the x^2 term. This means that the parabola opens downwards. Additionally, the 5 on the end represents the y-intercept, which indicates that the vertex of the parabola is at (0, 5).
2. The quadratic rule y = -x^2 + 5 also has a negative coefficient (-1) in front of the x^2 term. It also opens downwards and the vertex is at (0, 5).
3. The quadratic rule y = x^2 - 5 has a positive coefficient (1) in front of the x^2 term. This means that the parabola opens upwards. The -5 on the end indicates that the vertex of the parabola is at (0, -5).
4. The quadratic rule y = x^2 + 5 also has a positive coefficient (1) in front of the x^2 term. It opens upwards and the vertex is at (0, 5).
Based on the information provided, the quadratic rule that best represents the data in the table is option 4: y = x^2 + 5. This is because it has a positive coefficient and opens upwards, which matches the data description.