Just like you graph about any function: Pick some values for x, calculate the corresponding values for y, plot the points, join in a smooth curve.
There are infinitely many options. The equation could be a polynomial of degree greater than 1, or it could be a power function, a log function or any combination of these with trig functions. The problem is exacerbated by the fact that there is no clue in the question as to what a stands for.
A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.
That it is non-linear. If it is a graph of a polynomial, it would need to be a polynomial of odd order. But it could be the graph of the tangent function, or a combination of reciprocal functions over a limited domain. In fact the s shaped line, by itself, indicates very little.
false
no
The degree is equal to the maximum number of times the graph can cross a horizontal line.
There are infinitely many options. The equation could be a polynomial of degree greater than 1, or it could be a power function, a log function or any combination of these with trig functions. The problem is exacerbated by the fact that there is no clue in the question as to what a stands for.
A non-linear graph. It could be a polynomial (of a degree greater than 1), a power function, a logarithmic or trigonometric graph. In fact any mathematical function other than a linear equation.
A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.
With difficulty. Plot a graph of the polynomial and see where it crosses the x axis. If it does, then y=0 at that point, and (x-a) is a factor. Sometimes you might spot where the polynomial is zero just by trying various values.
That it is non-linear. If it is a graph of a polynomial, it would need to be a polynomial of odd order. But it could be the graph of the tangent function, or a combination of reciprocal functions over a limited domain. In fact the s shaped line, by itself, indicates very little.
An expression of polynomial degree 1 is a linear polynomial, typically written in the form ( ax + b ), where ( a ) and ( b ) are constants, and ( a \neq 0 ). The highest power of the variable ( x ) in this expression is 1, indicating that the graph of this polynomial is a straight line. Examples include ( 2x + 3 ) and ( -5x - 1 ).
An even function is symmetric about the y-axis. The graph to the left of the y-axis can be reflected onto the graph to the right. An odd function is anti-symmetric about the origin. The graph to the left of the y-axis must be reflected in the y-axis as well as in the x-axis (either one can be done first).
Either graph the polynomial on graph paper manually or on a graphing calculator. If it is a "y=" polynomial, then the zeroes are the points or point where the polynomial touches the x-axis. If it is an "x=" polynomial, then the zeroes are the points or point where the polynomial touches the y-axis. If it touches neither, then it has no zeroes.
An even degree refers to a polynomial in which the highest exponent of the variable is an even number, such as 0, 2, 4, etc. For example, in the polynomial ( f(x) = x^4 + 2x^2 + 1 ), the highest degree is 4, making it an even-degree polynomial. Even-degree polynomials typically have a U-shaped graph and can have either no real roots or an even number of real roots.
Easy. Same thing as the graph of f(x) = x^2 + 1 which have NO intercept.
The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.