Questions: The parabola (y=x^2+4) is obtained from the parabola (y=x^2) by which one of the following shifts? sideways right by 2 units upwards by 4 units sideways left by 2 units downwards by 4 units upwards by 2 units

The parabola (y=x^2+4) is obtained from the parabola (y=x^2) by which one of the following shifts?
sideways right by 2 units
upwards by 4 units
sideways left by 2 units
downwards by 4 units
upwards by 2 units

Transcript text: 3. The parabola $y=x^{2}+4$ is obtained from the parabola $y=x^{2}$ by which one of the following shifts? sideways right by 2 units upwards by 4 units sideways left by 2 units downwards by 4 units upwards by 2 units

Solution

Solution Steps

Step 1: Identify the Original and Transformed Functions

The original function is $ y = x^{2} $, and the transformed function is $ y = x^{2} + 4 $.

Step 2: Compare the Two Functions

The transformed function $ y = x^{2} + 4 $ is obtained by adding 4 to the original function $ y = x^{2} $. This addition affects the vertical position of the parabola.

Step 3: Determine the Type of Shift

Adding a constant to the original function results in a vertical shift. Since the constant is positive, the parabola shifts upwards by 4 units.