A quadratic function on a graph has the vertex at the point (-3, -2). Which of the...
Check the final answer first, then review the worked steps.
Problem
A quadratic function on a graph has the vertex at the point (-3, -2). Which of the following transformations translates the vertex to the point (0, 0)?
Answer
shift right 3 units and up 2 units
Step-by-step solution
- Identify the initial and target vertex coordinates: The initial vertex is at $(-3, -2)$ and the target vertex is at $(0, 0)$.
- Determine the horizontal shift: To move from an x-coordinate of $-3$ to an x-coordinate of $0$, we need to add $3$ to the x-coordinate. A positive change in the x-coordinate corresponds to a shift to the right. Therefore, the horizontal shift is $3$ units to the right. This can be represented as: $0 = -3 + \Delta x$, which gives $\Delta x = 3$.
- Determine the vertical shift: To move from a y-coordinate of $-2$ to a y-coordinate of $0$, we need to add $2$ to the y-coordinate. A positive change in the y-coordinate corresponds to a shift upwards. Therefore, the vertical shift is $2$ units up. This can be represented as: $0 = -2 + \Delta y$, which gives $\Delta y = 2$.
- Combine the shifts: The transformations required are a shift of $3$ units to the right and a shift of $2$ units up.
- Match with the given options: Comparing these transformations with the provided options, the correct one is "shift right 3 units and up 2 units".