QUESTION I Parabola - The graph of the form \( f(x)=a(x+p)^{2}+q \) 1.1 Draw the graphs of the equations below accorting to the Graph Papers indicated: First Graph Paper Original graph (M): \( y=x^{2} \) Graph 1: \( y=2 r^{2} \) Graph 2: \( y=\frac{1}{2} x^{2} \) Graph 3: \( y=-2 r^{2} \) Second Graph Paper Original graph (M):y= \( x^{2} \) Graph 1: \( y=x^{2}-4 \) Graph 2: \( y=x^{2}+2 \) Graph 3: \( y=2 r^{2}-4 \) Graph 4: \( y=\frac{1}{2} x^{2}+2 \)

To draw the graphs of the given equations, we will analyze each equation step by step. The original graph is \( y = x^2 \), which is a standard parabola opening upwards with its vertex at the origin (0,0). ### First Graph Paper 1. **Original Graph (M):** - Equation: \( y = x^2 \) - This is a standard parabola. 2. **Graph 1:** - Equation: \( y = 2x^2 \) - This graph is a vertical stretch of the original graph by a factor of 2. The vertex remains at (0,0), but the parabola opens upwards more steeply. 3. **Graph 2:** - Equation: \( y = \frac{1}{2}x^2 \) - This graph is a vertical compression of the original graph by a factor of 0.5. The vertex remains at (0,0), but the parabola opens upwards less steeply. 4. **Graph 3:** - Equation: \( y = -2x^2 \) - This graph is a vertical stretch of the original graph by a factor of 2, but it opens downwards. The vertex remains at (0,0). ### Second Graph Paper 1. **Original Graph (M):** - Equation: \( y = x^2 \) - This is the same standard parabola as before. 2. **Graph 1:** - Equation: \( y = x^2 - 4 \) - This graph is a downward shift of the original graph by 4 units. The vertex moves from (0,0) to (0,-4). 3. **Graph 2:** - Equation: \( y = x^2 + 2 \) - This graph is an upward shift of the original graph by 2 units. The vertex moves from (0,0) to (0,2). 4. **Graph 3:** - Equation: \( y = 2x^2 - 4 \) - This graph is a vertical stretch of the original graph by a factor of 2 and a downward shift by 4 units. The vertex moves from (0,0) to (0,-4). 5. **Graph 4:** - Equation: \( y = \frac{1}{2}x^2 + 2 \) - This graph is a vertical compression of the original graph by a factor of 0.5 and an upward shift by 2 units. The vertex moves from (0,0) to (0,2). ### Summary of Transformations - **Vertical Stretch/Compression:** Changes the steepness of the parabola. - **Vertical Shift:** Moves the graph up or down without changing its shape. ### Graphing To graph these equations, you would plot points for each equation and connect them smoothly to form the parabolas. The vertex and direction of opening (upward or downward) are key features to note. If you need visual representations of these graphs, please let me know, and I can assist with that as well!