Chapter 9: Q. 9.101 (page 942)

Find the maximum or minimum value of the quadratic function $f (x) = x^{2} - 8 x + 12$ .

Short Answer

Expert verified

The minimum value of the function $f (x) = x^{2} - 8 x + 12$ is $- 4$ .

Step by step solution

Step 1. Given information

Quadratic function is $f (x) = x^{2} - 8 x + 12$ .

We have to find the maximum or minimum.

Step 2. Identify maximum or minimum

The quadratic function $f (x) = a x^{2} + b x + c$ opens up if $a > 0$ and this function has a minimum.

In the function $f (x) = x^{2} - 8 x + 12$ , $a = 1$

since $a > 0$ , the parabola opens up and the function has a minimum.

Step 3. Find the vertex.

The vertex lies on the axis of symmetry $x = - \frac{b}{2 a}$ .

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

Find $f (4)$ .

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

Vertex is $(4, - 4)$ .

Step 4. Find minimum value.

Since the parabola has a minimum, the y -coordinate of the vertex is the minimum y -value of the quadratic equation. The minimum value of the quadratic is $- 4$ .

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Find the maximum or minimum value of the quadratic function $f (x) = x^{2} - 8 x + 12$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Identify maximum or minimum

Step 3. Find the vertex.

Step 4. Find minimum value.

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Find the maximum or minimum value of the quadratic function f(x)=x2-8x+12.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Identify maximum or minimum

Step 3. Find the vertex.

Step 4. Find minimum value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Calculus

Pure Maths

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the maximum or minimum value of the quadratic function $f (x) = x^{2} - 8 x + 12$ .