344293
Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

The function f(x) is a quadratic function and a limited table of values is provided
below. Write the equation of the quadratic polynomial in standard
form.

The Function Fx Is A Quadratic Function And A Limited Table Of Values Is Provided Below Write The Equation Of The Quadratic Polynomial In Standard Form class=

Sagot :

altavistard

Answer:

x^2 - x - 12

Step-by-step explanation:

The quadratic will have the form f(x) = ax^2 + bx + c

Note that when x = 0, y = -12.  Thus, we have f(0) = a(0)^2 + b(0) + c = -12, and the function (so far) is f(x) = ax^2 + bx - 12.

Arbitrarily choose two more ordered pairs from the table.  I've chosen (-3, 0) and (-4, 8).

For (-3, 0), the quadratic becomes 0 = a(-3)^2 + b(-3) - 12, or:

0 = 9a - 3b, and

For (4, 8), f(4) = 8 = a(4)^2 + b(8), or 8 = 16a + 8b, or 1 = 2a + b, or b = 1 - 2a

Solve 0 = 16a + 4b and b = 1 - 2a for a and b.

Let's use substitution:   Substitute b = 1 - 2a into 0 = 9a - 3b or 3a - b = 0:

3a - 1 - 2a = 0, or a = 1.

Since b = 1 - 2a, we get b = 1 - 2(1) = -1

and so a = 1, b = -1 and c = -12

Then the polynomial must be:  x^2 - x - 12

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.