Chapter 3: Q. 15 (page 174)

In Problems 15–17, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.
$f (x) = 3 x^{2} - 6 x + 4$

Short Answer

Expert verified

The quadratic function has a minimum value. The minimum value is $1$ .

Step by step solution

Step 1. Given information.

Determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.

$f (x) = 3 x^{2} - 6 x + 4$

Step 2. Compare the function.

Compare $f (x) = 3 x^{2} - 6 x + 4 to f (x) = a x^{2} + b x + c Then a = 3, b = - 6 and c = 4$

Since $a > 0$ , the graph of f opens up, so the vertex is a minimum value occurs at

$x = - \frac{b}{2 a} = - \frac{- 6}{2 (3)} = \frac{6}{6} = 1$

The minimum value is

$f (- \frac{b}{2 a}) = f (1) = 3 {(1)}^{2} - 6 (1) + 4 = 3 - 6 + 4 = 1$

Step 3. Conclusion.

The quadratic function has a minimum value. The minimum value is $1$ .

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In Problems 15–17, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.
$f (x) = 3 x^{2} - 6 x + 4$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Compare the function.

Step 3. Conclusion.

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In Problems 15–17, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.f(x)=3x2-6x+4

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Compare the function.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 15–17, determine whether the given quadratic function has a maximum value or a minimum value, and then find the value.
$f (x) = 3 x^{2} - 6 x + 4$