Chapter 3: Q 60. (page 156)

Determine without graphing whether the given quadratic function has a maximum value or a minimum value and then find the value.
$f (x) = 4 x^{2} - 4 x$

Short Answer

Expert verified

The minimum value is $- 1$ .

Step by step solution

Step 1. Given information.

The given function is $f (x) = 4 x^{2} - 4 x$ .

Step 2. Determine whether the graph of the function opens up or down.

Compare the given function $f (x) = 4 x^{2} - 4 x$ with $f (x) = a x^{2} + b x + c$ .

So, here $a = 4, b = - 4, c = 0$ .

If $a = 4 > 0$ , then the parabola opens up, which means that the function has a minimum value and it is the vertex.

Step 3. Determine the minimum value.

The minimum value occurs at $x = - \frac{b}{2 a}$ .

$\begin{array}{rcl} x & = & - \frac{- 4}{2 (4)} \\ = & \frac{1}{2} \end{array}$

The required minimum value is:

$\begin{array}{rcl} f (x) & = & 4 x^{2} - 4 x \\ f (\frac{1}{2}) & = & 4 {(\frac{1}{2})}^{2} - 4 (\frac{1}{2}) \\ = & 4 \times \frac{1}{4} - 4 \times \frac{1}{2} \\ = & 1 - 2 \\ = & - 1 \end{array}$

Step 4. Simplified answer.

Hence, the required minimum value is $- 1$ .

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x	$y = f (x)$
-2	-8
-1	-3
0	0
1	1
2	0

Determine without graphing whether the given quadratic function has a maximum value or a minimum value and then find the value.
$f (x) = 4 x^{2} - 4 x$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine whether the graph of the function opens up or down.

Step 3. Determine the minimum value.

Step 4. Simplified answer.

One App. One Place for Learning.

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Determine without graphing whether the given quadratic function has a maximum value or a minimum value and then find the value.fx=4x2-4x

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine whether the graph of the function opens up or down.

Step 3. Determine the minimum value.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Decision Maths

Statistics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Determine without graphing whether the given quadratic function has a maximum value or a minimum value and then find the value.
$f (x) = 4 x^{2} - 4 x$