Q52. The graph of the polynomial func... [FREE SOLUTION]

Chapter 7: Q52. (page 351)

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

Short Answer

Expert verified

The graph of the function $f (x) = 2 x (x - 4) (x + 1)$ is shown below.

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 $(5, 15)$ .

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

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

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

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

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

Now sketch the graph of the function (2).

Step 3. Interpretation from the graph.

From the graph it can be interpreted that the graph cuts x-axis at points $- 1, 0 and 4$ . Therefore, the real roots are $x = - 1, x = 0 鈥� and x = 4$ .

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91影视

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

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Interpretation from the graph.

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91影视

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

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Interpretation from the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Discrete Mathematics

Logic and Functions

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

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