Finite Math Examples

y = \frac{1}{3} x^{2}

$y = \frac{1}{3} x^{2}$

Step 1

Combine

\frac{1}{3}

$\frac{1}{3}$ and

x^{2}

$x^{2}$ .

y = \frac{x^{2}}{3}

$y = \frac{x^{2}}{3}$

Step 2

The largest exponent is the degree of the polynomial.

2

$2$

Step 3

Since the degree is even, the ends of the function will point in the same direction.

Even

Step 4

Identify the leading coefficient.

Tap for more steps...

Step 4.1

The leading term in a polynomial is the term with the highest degree.

\frac{x^{2}}{3}

$\frac{x^{2}}{3}$

Step 4.2

The leading coefficient in a polynomial is the coefficient of the leading term.

\frac{1}{3}

$\frac{1}{3}$

\frac{1}{3}

$\frac{1}{3}$

Step 5

Since the leading coefficient is positive, the graph rises to the right.

Positive

Step 6

Use the degree of the function, as well as the sign of the leading coefficient to determine the behavior.

1. Even and Positive: Rises to the left and rises to the right.

2. Even and Negative: Falls to the left and falls to the right.

3. Odd and Positive: Falls to the left and rises to the right.

4. Odd and Negative: Rises to the left and falls to the right

Step 7

Determine the behavior.

Rises to the left and rises to the right

Step 8