Precalculus Examples

$- x^{2} - 5 x + 6$

Step 1

Write $- x^{2} - 5 x + 6$ as a function.

$f (x) = - x^{2} - 5 x + 6$

Step 2

Identify the degree of the function.

Tap for more steps...

Step 2.1

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$- x^{2} \to 2$

$- 5 x \to 1$

$6 \to 0$

Step 2.2

The largest exponent is the degree of the polynomial.

$2$

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.

$- x^{2}$

Step 4.2

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

$- 1$

Step 5

Since the leading coefficient is negative, the graph falls to the right.

Negative

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.

Falls to the left and falls to the right

Step 8

Enter YOUR Problem