Analyzing Graphs of Polynomial Functions

Graph the polynomial function f\left(x\right)=x^4+3x^3-10x^2-24x. What is the maximum of this function?

Genesis, Adrean, and Anthony are participating in a city-wide math competition. They are faced with a task to graph polynomial functions. Which method do you think they employed from the given options?

• The old-school table method, just like their math teacher taught them

• The substitution method, because why not?

• The matrix method, sounds complicated right?

• The trial and error method, because sometimes guessing works too

Dominique, Elsa, and Aiden are on a quest to find a hidden artifact. They stumble upon an ancient inscription that reads, 'According to the location principle, between which consecutive integer values of X does the real zero of the function occur?' Can you help them decipher this clue?

• 1 and 2

• 0 and 1

• 2 and 3

• -2 and -1

Imagine Genesis, Jake, and Adrean are on a road trip driving towards a city. As their car approaches the city (which we'll call X), what happens to the intensity of the city's lights (considered as a polynomial function)?

• The light's intensity approaches a constant value

• The light's intensity approaches zero

• The light's intensity approaches negative infinity (gets darker)

• The light's intensity approaches positive infinity (gets brighter)

Elsa, Daniela, and Yoni are on a quest to find a hidden treasure. They stumbled upon a map with a graph. They deduced that the treasure is buried at the relative minima of the graph. Can you assist them in determining the x coordinate where the relative minima occurs on the graph?

• 1

• -1

• 3

• -3

Mayra, Sebastian, and Evelyn are on a mission to decode a secret message. They stumbled upon a coded message that can be deciphered using a polynomial function. To decode the next part of the message, they need to find the value of f(-2.5) for this function. Can you assist them?

• -16

• 0

• -41

• 3

In the above graph complete the following end behavior:

As x --> ∞, f(x) --> ____

As x --> - ∞, f(x) --> ____

• -∞

  -∞

• +∞

  -∞

• -∞

  +∞

• +∞

  +∞

There is a relative minimum at:

• x = -3.5

• x = -4

• x = -2.5

• x = -1

How many relative maximums does this function have?

• 1

• 2

• 3

• 4

How many REAL zeros can this function have?

• only 1

• must have 2

• 1-2

• 0-2