Chapter 3: Q 59. (page 156)

Determine without graphing whether the given quadratic function has a maximum value or a minimum value and then find the value.
$f (x) = - 3 x^{2} + 12 x + 1$

Short Answer

Expert verified

The maximum value is $13$ .

Step by step solution

Step 1. Given information.

The given function is $f (x) = - 3 x^{2} + 12 x + 1$ .

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

Compare the given function $f (x) = - 3 x^{2} + 12 x + 1$ with $f (x) = a x^{2} + b x + c$ .

So, $a = - 3, b = 12, c = 1$ .

If $a = - 3 < 0$ , then the parabola opens down, which means that the function has a maximum value and it is the vertex.

Step 3. Determine the minimum value.

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

role="math" localid="1646460944766" $\begin{array}{rcl} x & = & - \frac{12}{2 (- 3)} \\ = & \frac{12}{6} \\ = & 2 \end{array}$

The required maximum value is:

$\begin{array}{rcl} f (x) & = & - 3 x^{2} + 12 x + 1 \\ f (2) & = & - 3 {(2)}^{2} + 12 (2) + 1 \\ = & - 12 + 24 + 1 \\ = & 13 \end{array}$

Step 4. Simplified answer.

Hence, the required maximum value is $13$ .

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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.
$f (x) = - 3 x^{2} + 12 x + 1$

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.

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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=-3x2+12x+1

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

Logic and Functions

Mechanics Maths

Applied Mathematics

Pure Maths

Geometry

Calculus

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.
$f (x) = - 3 x^{2} + 12 x + 1$