The basic idea is that a graph of an equation is the pictorial representation of all of the points that satisfy the equation. So, where the graph of one equation crosses the graph of another, the point where they cross will satisfy both equations.

Finding a solution means finding values of the variables that satisfy all of the equations. Hence, the point of intersection is the solution of the equations.

To solve linear equations by graphing, graph each of the equations. Then find the coordinates of the point where the lines intersect. Those coordinates are the solution to the equations.

If the solution is not at a grid point on the graph, determining its exact value may not be easy. This can often be aided by a graphing calculator, which can often tell you the point of intersection to calculator accuracy.

If the lines don't intersect, there are no solutions. If they are the same line (intersect everywhere), then there are an infinite number of solutions.

3 0

3 years ago

Explain why the graph of quadratic function could not contain both a minimum vertex and a maximum vertex at the same time.

KonstantinChe [14]

A quadratic function is a function of the form $f(x)=ax^2+bx+c$ . The vertex, $(h,k)$ of a quadratic function is determined by the formula: $h= \frac{-b}{2a}$ and $k=f(h)$ ; where $h$ is the x-coordinate of the vertex and $k$ is the y-coordinate of the vertex. The value of $a$ determines if the parabola opens upward or downward; if $a$ is positive, the parabola opens upward and the vertex is the minimum value, but if $a$ is negative the graph opens downward and the vertex is the maximum value. Since the quadratic function only has one vertex, it could not contain both a minimum vertex and a maximum vertex at the same time.

3 0

3 years ago