Polynomial graphing calculator

This calculator graphs polynomial functions. All polynomial characteristics, including polynomial roots (x-intercepts), sign, local maxima and minima, growing and decreasing intervals, points of inflection, and concave up-and-down intervals, can be calculated and graphed.

Sketch the graph of the polynomial function $p (x) = x^{2}$

solution

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explanation

STEP 1:Find the x-intercepts

To find the x-intercepts solve, the equation $x^{2} = 0$

The solution of this equation is:

x = 0

(you can use the step-by-step polynomial equation solver to see a detailed explanation of how to solve the equation)

STEP 2:Find the y-intercepts

To find the y-intercepts, substitute $x = 0$ into $p (x) = x^{2}$ , so:

Y inercept = p (0) = 0

STEP 3:Find the end behavior

The end behavior of a polynomial is the same as the end behavior of a leading term.

x \to - \infty lim (x^{2}) = x \to - \infty lim x^{2} = \infty

The graph starts in the upper-left corner.

x \to \infty lim (x^{2}) = x \to \infty lim x^{2} = \infty

The graph ends in the upper-right corner.

STEP 4:Find the turning points

To determine the turning point, we need to find the first derivative of $p (x)$ :

p^{'} (x) = 2 x

The x coordinate of the turning point is located at the zeros of the first derivative

p^{'} (x) = 0

x = 0

(cleck here to see a explanation of how to solve the equation)

To find the y coordinate, substitute the above value into $p (x)$

for x = 0 \Rightarrow p (0) = 0

So the turning point is:

(0, 0)

Polynomial graphing calculator

Explore and graph polynomial functions.
help ↓↓ examples ↓↓

0123456789+–^xC ✖

Input polynomial:

Examples:

x^2+3x-4

2x^3-3x^2-2x+3

x^4/12-x^3/3-7x^2/12+5x/6

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RESOURCES

1. A video tutorial showing how to graph a polynomial using end behavior.

2. Graphs of polynomial using its zeros and end behavior.

3. Desmos is a great tool for graphing all kinds of functions.

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Polynomial graphing calculator

Sketch the graph of the polynomial function p(x)=x2

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Sketch the graph of the polynomial function $p (x) = x^{2}$