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How do you find the end behavior of 2x5 plus 5x4-2x3-7x2-4x-12?
f(x) = 2x5 + 5x4 - 2x3 - 7x2 -4x - 12 We use the Leading Coefficient Test to determine the graph's end behavior. Because the degree of f(x) is odd (n = 5) and the leading coefficient, 2, is positive, the graph falls to the left and rises to the right.
What happens to the graph as the coefficient increases?
Most graphs will become steeper as the coefficient increases.
The graph of a line goes up and to the right when?
For a straight line graph, if the equation of the graph is written is the slope-intercept form, then the line goes up and to the right when the coefficient of x is positive.
How do you complete the square when the leading coefficient is not 1?
What is a possible leading coefficient and degree for a polynomial starting in quadrant 3 and ending in quadrant 4?
Leading coefficient: Negative. Order: Any even integer.
How does changing the sign of the leading coefficient in an equation of the form y equals ax2 affect its graph?
It gets reflected in the x-axis.
When an odd function has a negative leading coefficient what happens to the graph?
the left end of the graph is going in a positive direction and the right end is going in a negative direction.
What is the leading coefficient of each fungtion?
what is the leading coefficient -3x+8
How do you find zeros when the leading coefficient is one?
The answer depends on the what the leading coefficient is of!
How do you find the end behavior of 2x5 plus 5x4-2x3-7x2-4x-12?
f(x) = 2x5 + 5x4 - 2x3 - 7x2 -4x - 12 We use the Leading Coefficient Test to determine the graph's end behavior. Because the degree of f(x) is odd (n = 5) and the leading coefficient, 2, is positive, the graph falls to the left and rises to the right.
What happens to the graph as the coefficient increases?
Most graphs will become steeper as the coefficient increases.
What is leading coefficient?
It is the coefficient of the highest power of the variable in an expression.
The graph of a line goes up and to the right when?
For a straight line graph, if the equation of the graph is written is the slope-intercept form, then the line goes up and to the right when the coefficient of x is positive.
How does changing the signs of the coefficients affect the graph of a polynomial?
For a polynomial of order n there are n+1 coefficients that can be changed. There are therefore 2^(n+1) related polynomials with coefficients of the same absolute values. All these generate graphs whose shapes differ.If only the constant coefficient is switched, the graph does not change shape but moves vertically. If every coefficient is switched then the graph is reflected in the horizontal axis. For all other sign changes, there are intermediate changes in the shape of the graph.
What is the leading coefficient in a polynomial?
It is the number (coefficient) that belongs to the variable of the highest degree in a polynomial.
How do you find transformations in an equation?
To find transformations in an equation, you can look for changes in the coefficients and constants that affect the position, size, or shape of the graph. For example, a coefficient before the x term will affect the stretch or compression of the graph, while a constant added or subtracted will affect the vertical shift. Additionally, changes inside functions (such as squaring or square rooting) can also indicate transformations.
