 Which graph shows a mixed-degree system with only one solution? If a mixed-degree system has more than one solution, it has two solutions. In this case, the solution is the value that is true for all of the equations in the system.

## Graph of \$y=x2\$ with exactly one solution

A graph of \$y=x2\$ with exactly a single solution can be drawn for a system of equations with only one solution. The graph shows a point on the system where the two equations intersect. The point is called the solution and it appears to be (1, 2) where the two equations meet.

If the inequality is f(x), the solution is f(x). The left hand side of the equation is f(x), and the right hand side is g(x). If you substitute a and b with zero, then the inequality is true.

You can also graph this equation by substituting a number for x and solving for y. In this case, if x = 1, then the y-value of the coordinates will be 6. Other points on the graph will be (1, 6), and (2, 9).

The graph of \$y=x2 with exactly a solution is a parabola, in which the curve opens upward and closes downward. The vertex is the highest point on the curve. The curve’s concavity depends on the value of a, which corresponds to the rate at which it opens. A larger value of a implies a faster rate of function growth.

A graph of \$y=x2 with exactly a solution has an axis of symmetry at x = -3. By extending that axis four units to the left, we can get y=x2 -12, which is a vertex-form parabola.

When the vertex x=-1, the x-coordinate of the vertex y=x2 equals 7. Likewise, the x-coordinate y=-7 for all x is -1. The axis of symmetry also gives the x-coordinate. This is the same as the axis of symmetry in a general quadratic.

A graph of \$y=x2 with exactly one solution is a parabola with an axis of symmetry at x = 0. A graph of a parabola can be drawn in any coordinate system by applying transformations. It can also be sketched using transformations. You can also consider the material as an extension and use calculus to find the vertex of the graph.

## Graph of \$y=x3\$ with exactly one solution

Graph of \$y=x3 with exactly one solution has two solutions. The given function, f(x), goes through the origin (0,0) while the parent function, g(x), goes through the origin x-x-1. In both cases, the vertical shift is one unit.

The graph of two equations may not be the same, but the point of intersection is the same. A solution to one equation is also a solution to the other. Hence, a graph of \$y=x3\$ with exactly a single solution is a graph with the same points as the other equation.

The y-intercept of this equation is (0,-7) and the x-intercept appears to be 1.5. However, evaluating the function at zero gives f(0) = -7, which is not in the domain of the function. Likewise, the x-intercept appears to be 1.5, but it could also be outside of the viewing rectangle.

## Graph of \$y=x4\$ with exactly one solution

A graph of \$y=x4\$ with exactly 1 solution shows the solution of two unknowns. For example, if x = 25 and y = -4x, the graph would be below the x-axis and between the points -2 and 2.

When two equations have the same graph, the two solutions are equivalent. Therefore, if a point on a graph is the solution to one equation, then it is also the solution to the other. If two graphs have the same equation, the two solutions must intersect at the same point.

To solve this equation, first determine the axis of symmetry. In the first case, the y-intercept is at (0,-7), which is a very simple solution. Then, determine the x-intercept, which appears to be 1.5. However, it might be outside the viewing rectangle.