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A graph crosses the x-axis at points where the value of the function is zero, meaning the y-coordinate is zero (f(x) = 0). These points can be found by solving the equation of the function for when y = 0. The graph crosses the y-axis at the point where x is zero, which corresponds to the value of the function at that point (f(0)). Thus, the y-intercept is found by evaluating the function at x = 0.
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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.
What is the place or point where a graph crosses the axis is known as?
The point where a graph crosses an axis is known as an "intercept." Specifically, the x-intercept is where the graph crosses the x-axis, while the y-intercept is where it crosses the y-axis. These points indicate the values of the variable when the other variable is zero.
In given figure graph of polynomial x is given find the zero of polynomial?
To find the zeros of the polynomial from the given graph, identify the points where the graph intersects the x-axis. These intersection points represent the values of x for which the polynomial equals zero. If the graph crosses the x-axis at specific points, those x-values are the zeros of the polynomial. If the graph merely touches the x-axis without crossing, those points indicate repeated zeros.
What part of a graph can you get from the factor of the polynomial?
The factors of a polynomial provide information about the roots or x-intercepts of the graph. Specifically, if a polynomial is factored into the form ( (x - r_1)(x - r_2)...(x - r_n) ), then the values ( r_1, r_2, ..., r_n ) are the points where the graph intersects the x-axis. Additionally, the multiplicity of each factor indicates the behavior of the graph at those intercepts, such as whether the graph crosses or touches the x-axis at those points.
Where an equation crosses the horizontal axis?
An equation crosses the horizontal axis at points where the output value (usually represented by (y)) is zero. These points are known as the roots or x-intercepts of the equation. To find these points, you set the equation equal to zero and solve for the variable, typically represented as (x). Graphically, this represents the points where the graph of the equation intersects the x-axis.
How do you find the zeros in an equation by looking on a graph?
They are all the points where the graph crosses (or touches) the x-axis.
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.
What does the discriminant tell you about the graph?
Whether the graph has 0, 1 or 2 points at which it crosses (touches) the x-axis.
What do the zeros of a polynomial function represent on a graph?
The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.
What is the points where a graph crosses the x-axis and y-axis?
It is at point of origin which is at (0, 0)
What is the point at which a graph crosses the x-axis?
For a line, this is the x-intercept. For a polynomial, these points are the roots or solutions of the polynomial at which y=0.
Where do you find the roots when looking at a parabola?
-- 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.
Where an equation crosses the horizontal axis?
An equation crosses the horizontal axis at points where the output value (usually represented by (y)) is zero. These points are known as the roots or x-intercepts of the equation. To find these points, you set the equation equal to zero and solve for the variable, typically represented as (x). Graphically, this represents the points where the graph of the equation intersects the x-axis.
Where the graph crosses the y-axis?
x = 0
The x value of the point where a graph crosses the x axis?
It is the x intercept
What is the difference of x-intercept and y-intercept?
The x- and y-intercepts of a function are the points at which the graph of the function crosses respectively the x- and y-axis (ie. y=0 and x=0).
How can tbe x intercept and y intercept be used to graph a linear equation?
To graph a linear equation, the x-intercept and y-intercept provide two key points on the line. The x-intercept is where the line crosses the x-axis (where y = 0), and the y-intercept is where it crosses the y-axis (where x = 0). By plotting these two points on a Cartesian plane and drawing a straight line through them, you can accurately represent the linear equation. This method is particularly useful for quickly sketching the graph without needing to find additional points.
