graph the system
y>x^2
y>_5x+4
Here's the graph for the system. The blue plot represents the equation y>x^2 and the orange one represents y>=5x+4. The green area represents the solution to the system, where y is greater than both x^2 and 5x+4.
Graph:
https://www.desmos.com/calculator/cmpjvk2peb
Remember, since y > x^2 and y >= 5x + 4, representative points would not be on the graph for the first inequality but for the second one.
How this graph is labeled?
The x-axis and y-axis are clearly marked. X-axis represents the 'x' values while the y-axis represents 'y' values. The plot has been scaled accordingly, each grid cell increases by 1. The highlighted region shows the values of '(x,y)' which satisfies both of the inequalities given in the system.
To graph the system of inequalities y > x^2 and y ≥ 5x + 4, we will graph each inequality separately and shade the appropriate region.
1. Graphing the inequality y > x^2:
- Start by graphing the equation y = x^2, which is a parabola opening upwards.
- Choose a few values for x and calculate the corresponding values of y using the equation.
- Plot the points on a graph and connect them to form a smooth curve for the parabola.
- Since y > x^2, the region above the parabola is the solution area.
- Shade the region above the curve to represent the inequality y > x^2.
2. Graphing the inequality y ≥ 5x + 4:
- Start by graphing the equation y = 5x + 4, which is a straight line.
- Choose a few values for x and calculate the corresponding values of y using the equation.
- Plot the points on a graph and connect them to form a straight line.
- Since y ≥ 5x + 4, the region above or on the line is the solution area.
- Shade the region above or on the line to represent the inequality y ≥ 5x + 4.
Finally, the intersection of the shaded regions from both inequalities will give us the solution to the system of inequalities.
Note: Without specific numerical values for x and y, the graph will be represented with the equations as described above.
To graph the system of inequalities y > x^2 and y ≥ 5x + 4, follow the steps below:
Step 1: Graph the equation y = x^2.
- Start by creating a coordinate plane (x and y-axis) with a range that covers the area of interest.
- Plot the graph of the equation y = x^2. You can do this by choosing different x-values, calculating the corresponding y-values (using the equation y = x^2), and plotting the points on the graph.
Step 2: Graph the equation y = 5x + 4.
- Using the same coordinate plane from Step 1, plot the points for y = 5x + 4. Choose different x-values, calculate the corresponding y-values, and plot the points.
Step 3: Shade the region above the graph of y = x^2.
- Since the inequality is y > x^2, shade the region above the graph of y = x^2 using a dashed line.
Step 4: Shade the region above or on the graph of y = 5x + 4.
- Since the inequality is y ≥ 5x + 4, shade the region above or on the graph of y = 5x + 4 using a solid line.
Step 5: Identify the overlapping shaded region.
- The overlapping region between the shaded region above the graph of y = x^2 and the shaded region above or on the graph of y = 5x + 4 represents the solution to the system of inequalities.
Note: If there is no overlapping region, it means there are no common solutions for the two inequalities.