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How can a graph be used to determine how many solutions an equation has?
Count the number of many times the graph intersects the x-axis. Each crossing point is a root of the equation.
How do you use a graph to determine 3 solutions of an equation?
To determine three solutions of an equation using a graph, first plot the equation on a coordinate plane. Identify the points where the graph intersects the x-axis; these x-values represent the solutions of the equation. Each intersection point corresponds to a solution, so you can read the x-coordinates of these points to find the three solutions. Ensure that the graph is drawn accurately for precise identification of the solutions.
How are the graph of an equation and the set of all solutions of an equation related?
The coordinates of every point on the graph, and no other points, are solutions of the equation.
Explain how the number of solutions for a quadratic equation relates to the graph of the function?
The number of solutions for a quadratic equation corresponds to the points where the graph of the quadratic function intersects the x-axis. If the graph touches the x-axis at one point, the equation has one solution (a double root). If it intersects at two points, there are two distinct solutions, while if the graph does not touch or cross the x-axis, the equation has no real solutions. This relationship is often analyzed using the discriminant from the quadratic formula: if the discriminant is positive, there are two solutions; if zero, one solution; and if negative, no real solutions.
What has an infinite number of solutions?
A single equation in two variables is, for example. Its graph is a line, and every point on the line is a solution.
How can a graph be used to determine how many solutions an equation has?
Count the number of many times the graph intersects the x-axis. Each crossing point is a root of the equation.
How do you use a graph to determine 3 solutions of an equation?
To determine three solutions of an equation using a graph, first plot the equation on a coordinate plane. Identify the points where the graph intersects the x-axis; these x-values represent the solutions of the equation. Each intersection point corresponds to a solution, so you can read the x-coordinates of these points to find the three solutions. Ensure that the graph is drawn accurately for precise identification of the solutions.
A graph of the set of ordered pairs that are solutions of the equation?
Graph of an equation.
How are the graph of an equation and the set of all solutions of an equation related?
The coordinates of every point on the graph, and no other points, are solutions of the equation.
How do you determine the solutions on a graph for a quadratic equation?
The X-Intercepts are the solutions. If you have an algebra calculator, you can usually find them by going to CALC>Zero>enter the left and right boundaries for each side.
An equation where the graph of all solutions lies on a line?
If it is a straight line, then the equation is linear.
What is an equation where the graph of all solutions lies on a line?
There are an infinite number of equations that meet that requirement. One of them is y = x
What has an infinite number of solutions?
A single equation in two variables is, for example. Its graph is a line, and every point on the line is a solution.
How are the real solutions of a quadratic equation related to the graph of the quadratic function?
The real solutions are the points at which the graph of the function crosses the x-axis. If the graph never crosses the x-axis, then the solutions are imaginary.
How you find the solution of a quadratic equation by graphing its quadratic equation?
When you graph the quadratic equation, you have three possibilities... 1. The graph touches x-axis once. Then that quadratic equation only has one solution and you find it by finding the x-intercept. 2. The graph touches x-axis twice. Then that quadratic equation has two solutions and you also find it by finding the x-intercept 3. The graph doesn't touch the x-axis at all. Then that quadratic equation has no solutions. If you really want to find the solutions, you'll have to go to imaginary solutions, where the solutions include negative square roots.
An equation where the graph of all solutions lies on a line is called?
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What does the graph of a line represent?
It represents all solutions to the linear equation.
