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Can the leading coefficient of a polynomial function be a fraction?
Yes, the leading coefficient of a polynomial function can be a fraction. A polynomial is defined as a sum of terms, each consisting of a coefficient (which can be any real number, including fractions) multiplied by a variable raised to a non-negative integer power. Thus, the leading coefficient, which is the coefficient of the term with the highest degree, can indeed be a fraction.
If the degree of a polynomial function is even and the leading coefficient is negative then what will happen to the ends?
If a polynomial function has an even degree and a negative leading coefficient, the ends of the graph will both point downward. This means that as the input values approach positive or negative infinity, the output values will also approach negative infinity. In summary, the graph will have a "U" shape that opens downwards.
What is conactivity of parabola?
The concavity of a parabola refers to the direction it opens: upwards or downwards. A parabola opens upwards if its leading coefficient (the coefficient of the quadratic term) is positive, resulting in a "U" shape. Conversely, it opens downwards if the leading coefficient is negative, forming an "n" shape. The vertex of the parabola represents the point of minimum or maximum value, depending on its concavity.
How do you find zeros when the leading coefficient is one?
The answer depends on the what the leading coefficient is of!
What is the leading coefficient of each fungtion?
what is the leading coefficient -3x+8
Can the leading coefficient of a polynomial function be a fraction?
Yes, the leading coefficient of a polynomial function can be a fraction. A polynomial is defined as a sum of terms, each consisting of a coefficient (which can be any real number, including fractions) multiplied by a variable raised to a non-negative integer power. Thus, the leading coefficient, which is the coefficient of the term with the highest degree, can indeed be a fraction.
If the degree of a polynomial function is even and the leading coefficient is negative then what will happen to the ends?
If a polynomial function has an even degree and a negative leading coefficient, the ends of the graph will both point downward. This means that as the input values approach positive or negative infinity, the output values will also approach negative infinity. In summary, the graph will have a "U" shape that opens downwards.
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 conactivity of parabola?
The concavity of a parabola refers to the direction it opens: upwards or downwards. A parabola opens upwards if its leading coefficient (the coefficient of the quadratic term) is positive, resulting in a "U" shape. Conversely, it opens downwards if the leading coefficient is negative, forming an "n" shape. The vertex of the parabola represents the point of minimum or maximum value, depending on its concavity.
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.
What is the end behavior of a function?
The end behavior of a function is how the function acts as it approaches infinity and negative infinity. All even functions such as x^2 approach infinity in the y-axis as x approaches infinity and odd functions such as x^3 approach positive infinity in the y- axis as x approaches positive infinity and negative infinity in the y- axis as x approaches negative infinity. If their is a negative leading coefficient then it is just flipped.
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!
Polynomial function has a root of and ndash6 with multiplicity 3 and a root of 2 with multiplicity 4. If the function has a negative leading coefficient and is of odd degree which could be the graph o?
The polynomial function can be expressed as ( f(x) = -k(x + 6)^3(x - 2)^4 ), where ( k > 0 ). Given that it has a root of -6 with multiplicity 3 and a root of 2 with multiplicity 4, the overall degree of the polynomial is 7 (odd). With a negative leading coefficient, the graph will fall to the right and rise to the left. Additionally, at ( x = -6 ), the graph will have a local maximum, and at ( x = 2 ), it will have a local minimum.
What is leading coefficient?
It is the coefficient of the highest power of the variable in an expression.
What does a function on a graph look like?
A function is just a fancy name for a math problem. It could be a straight line or it could be a parabola or even some thing else. The key to knowing what it looks like is the leading coefficient. What is the highest power of x? Is it positive or negative? An x with the power of one will be a straight line at an angle.
What is a polynomial function f of least degree that has rational coefficient a leading coefficient of 1 and the given zeros -7 -4?
A polynomial function of least degree with rational coefficients and a leading coefficient of 1 that has the zeros -7 and -4 can be constructed using the fact that if ( r ) is a zero, then ( (x - r) ) is a factor. Therefore, the polynomial can be expressed as ( f(x) = (x + 7)(x + 4) ). Expanding this, we get ( f(x) = x^2 + 11x + 28 ). Thus, the polynomial function is ( f(x) = x^2 + 11x + 28 ).
