Chapter 10: Q. 319 (page 1238)

In the following exercises, find the minimum or maximum value.
$y = 7 x^{2} + 14 x + 6$

Short Answer

Expert verified

The minimum value of the function is $- 1$ and it occurs when $x = - 1$ .

Step by step solution

Given information

The given expression is: $y = 7 x^{2} + 14 x + 6$ .

Determine the minimum or maximum value.

Comparing the given function with standard form $f (x) = a x^{2} + b x + c$ , the values are $a = 7$ , $b = 14$ , $c = 6$ .

Because the value of the leading coefficient ais positive, so the parabola opens up.

The quadratic function has a minimum.

Determine the equation of axis of symmetry.

The axis of symmetry is the vertical line given by $x = - \frac{b}{2 a}$ .

Substituting the value of a and b.

$x = - \frac{14}{2 (7)}$

$= - \frac{14}{14} = - 1$

The equation of the axis of symmetry is $x = - 1$ .

Determine the minimum value of function.

Evaluate $y (- 1)$ by substituting $x = - 1$ in $y = - x^{2} + 4 x - 5$ .

$y = 7 {(- 1)}^{2} + 14 (- 1) + 6 = 7 - 14 + 6 = - 7 + 6 = - 1$

So, the vertex is $(- 1, - 1)$ .

The minimum value of the function is $- 1$ and it occurs when $x = - 1$ .

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In the following exercises, find the minimum or maximum value.
$y = 7 x^{2} + 14 x + 6$

Short Answer

Step by step solution

Given information

Determine the minimum or maximum value.

Determine the equation of axis of symmetry.

Determine the minimum value of function.

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Most popular questions from this chapter

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In the following exercises, find the minimum or maximum value.y=7x2+14x+6

Short Answer

Step by step solution

Given information

Determine the minimum or maximum value.

Determine the equation of axis of symmetry.

Determine the minimum value of function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Calculus

Geometry

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, find the minimum or maximum value.
$y = 7 x^{2} + 14 x + 6$