They are all the points where the graph crosses (or touches) the x-axis.
The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
by synthetic division and quadratic equation
From the equation, the y intercept is simply determined by setting x = 0. The x intercept(s) are generally much harder to find: you will need to find the solutions of y = 0 [or f(x) = 0]. From the graph the intercepts are the coordinates of the points at which the graph crosses the axes.
Graph the equation then find the x intercepts.
At the x-intercept on the graph of the equation, y=0. Take the equation, set 'y' equal to zero, and solve the equation for 'x'. The number you get is the x-intercept.
You find the equation of a graph by finding an equation with a graph.
The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
when the equation is equal to zero. . .:)
It's actually quite hard to graph complex numbers - you would need a four-dimensional space to graph them adequately. I believe it's more convenient to find zeros analytically for such functions.
-- The roots of a quadratic equation are the values of 'x' that make y=0 . -- When you graph a quadratic equation, the graph is a parabola. -- The points on the parabola where y=0 are the points where it crosses the x-axis. -- If it doesn't cross the x-axis, then the roots are complex or pure imaginary, and you can't see them on a graph.
by synthetic division and 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.
You can either measure or estimate the coordinates visually from the graph, or solve the equation underlying the graph.
Set 'x' equal to zero, and solve the remaining equation for 'y'.
Select any value for one of the variables in the graph and solve the equation to get the other variable.
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In the same coordinate space, i.e. on the same set of axes: -- Graph the first equation. -- Graph the second equation. -- Graph the third equation. . . -- Rinse and repeat for each equation in the system. -- Visually examine the graphs to find the points (2-dimension graph) or lines (3-dimension graph) where all of the individual graphs intersect. Since those points or lines lie on the graph of each individual graph, they are the solution to the entire system of equations.