Chapter 7: Q51. (page 351)

The graph of the polynomial function $f (x) = a x (x - 4) (x + 1)$ passes through the point $(5, 15)$ . Re-write the function as the cubic function.

Short Answer

Expert verified

The function in cubic notation is written as $f (x) = 2 x^{3} - 6 x^{2} - 8 x$ .

Step by step solution

Step 1. Write down the given information.

It is given that the graph of the polynomial function $f (x) = a x (x - 4) (x + 1)$ passes through the point $(5, 15)$ . Therefore, the point $(5, 15)$ will satisfy,

$f (x) = a x (x - 4) (x + 1) . . . . (1)$

Step 2. Calculation.

Since the graph of the polynomial function $f (x) = a x (x - 4) (x + 1)$ passes through the point $(5, 15)$ . Therefore, the point $(5, 15)$ will satisfy $f (x) = a x (x - 4) (x + 1)$ .

$\begin{matrix} 15 = a (5) ((5) - 4) ((5) + 1) \\ 15 = 30 a \\ a = \frac{1}{2} \end{matrix}$

Plugging $a = \frac{1}{2}$ in (1),

$f (x) = 2 x (x - 4) (x + 1) . . . . (2)$

To write the function in cubic notation, multiply the respective terms of (2). Therefore, from (2).

$\begin{matrix} f (x) = 2 x (x - 4) (x + 1) \\ = 2 x^{3} - 6 x^{2} - 8 x \end{matrix}$

Step 3. Conclusion.

The function in cubic notation is written as $f (x) = 2 x^{3} - 6 x^{2} - 8 x$ .

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The graph of the polynomial function $f (x) = a x (x - 4) (x + 1)$ passes through the point $(5, 15)$ . Re-write the function as the cubic function.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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The graph of the polynomial function fx=axx-4x+1 passes through the point 5,15. Re-write the function as the cubic function.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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The graph of the polynomial function $f (x) = a x (x - 4) (x + 1)$ passes through the point $(5, 15)$ . Re-write the function as the cubic function.