describe how you can use the graph of y=x^2 to graph the given function.
y=2x^2 + 3
y=-3/4x^2 + 5
To graph the given functions, you can start by understanding the behavior of the basic graph of y = x^2.
The graph of y = x^2 is a parabola that opens upward with its vertex at the origin (0,0). As you move to the left or right along the x-axis, the y-values increase.
To graph y = 2x^2 + 3:
1. Start with the basic graph of y = x^2 and plot the vertex at (0,0).
2. Since the coefficient in front of x^2 is 2, the graph will stretch vertically by a factor of 2. For each x-value, multiply the y-value by 2 to get the corresponding y-value for the new equation.
3. Next, shift the entire graph up by 3 units. Add 3 to each y-value to get the final coordinates for the graph of y = 2x^2 + 3.
To graph y = -(3/4)x^2 + 5:
1. Again, start with the basic graph of y = x^2 and plot the vertex at (0,0).
2. Since the coefficient in front of x^2 is -(3/4), the graph will be reflected in the x-axis and stretched vertically by a factor of 3/4. For each x-value, multiply the y-value by 3/4 and then negate it (multiply by -1).
3. Finally, shift the entire graph up by 5 units. Add 5 to each y-value to get the final coordinates for the graph of y = -(3/4)x^2 + 5.
By following these steps, you can effectively graph any function that is based on the basic graph of y = x^2.