Question

Sketch the graph and name the solution points of the following system.

y = |x| + 3
y = x^(2) + 3

Answer 1

To sketch the graph and name the solution points of the system consisting of the equations y = |x| + 3 and y = x^2 + 3, pick values for x and solve for y. Plot the points on a coordinate plane and draw a curve to connect them. The solution points are the coordinates where the graph intersects the axes or other points of interest.

Step-by-step explanation:

To sketch the graph and name the solution points of the system consisting of the equations y = |x| + 3 and y = x^2 + 3, you can follow these steps:

1. Pick some x-values and plug them into each equation to find the corresponding y-values. For example, when x = -2, the first equation gives y = |-2| + 3 = 2 + 3 = 5, and the second equation gives y = (-2)^2 + 3 = 4 + 3 = 7.
2. Plot the points obtained from step 1 on a coordinate plane.
3. Draw a smooth curve to connect the plotted points. The resulting graph will represent the solution to the system of equations.
4. The solution points are the coordinates of the points where the graph intersects the coordinate axes, or any other points of interest such as intersections or turning points.