Chapter 3: Q. 16 (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.
$f (x) = - x^{2} + 8 x - 4$

Short Answer

Expert verified

The quadratic function has a maximum value. The maximum value is 12.

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.

$f (x) = - x^{2} + 8 x - 4$

Step 2. Compare the function.

Compare

$f (x) = - x^{2} + 8 x - 4 to f (x) = a x^{2} + b x + c Then a = - 1, b = 8 and c = - 4$

Since $a < 0$ the graph of f opens down, so the vertex is a maximum value occurs at

$x = - \frac{b}{2 a} = - \frac{8}{2 (- 1)} = 4$

The maximum value is

$f (- \frac{b}{2 a}) = f (4) = - 4^{2} + 8 (4) - 4 = - 16 + 32 - 4 = 12$

Step 3. Conclusion.

The quadratic function has a maximum value. The maximum value is 12.

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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.
$f (x) = - x^{2} + 8 x - 4$

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)=-x2+8x-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

Decision Maths

Geometry

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

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.
$f (x) = - x^{2} + 8 x - 4$