- #1
swechan02
- 5
- 0
Find the equations of the lines that are tangent to both curves simultaneously:y=(x^2) +1 and y = - (x^2)?
The equation y = x^2 + 1 is a quadratic equation where the y-value is equal to the square of the x-value plus 1. This equation creates a parabola when graphed.
To graph y = x^2 + 1, you can create a table of values by choosing different x-values and plugging them into the equation to find the corresponding y-values. Then, plot the points on a coordinate plane and connect them to create a parabola.
The equation y = -x^2 is a quadratic equation where the y-value is equal to the negative square of the x-value. This equation also creates a parabola when graphed, but it is reflected over the x-axis compared to y = x^2.
To graph y = -x^2, you can follow the same steps as graphing y = x^2 + 1, but the parabola will be reflected over the x-axis. You can also use the symmetry of the graph to plot points on one side and then reflect them over the x-axis to complete the graph.
The two equations y = x^2 + 1 and y = -x^2 are related because they are both quadratic equations that create parabolas when graphed. However, they are reflections of each other over the x-axis. Additionally, y = x^2 + 1 has a positive leading coefficient, which means the parabola opens upwards, while y = -x^2 has a negative leading coefficient, which means the parabola opens downwards.