Q14. Write the equation y=12x2+12x-8 ... [FREE SOLUTION]

Chapter 8: Q14. (page 424)

Write the equation $y = \frac{1}{2} x^{2} + 12 x - 8$ in standard form.

Short Answer

Expert verified

The required form of the equation in standard form $y = a {(x - h)}^{2} + k$ is $y = \frac{1}{2} {(x + 12)}^{2} - 80$ where $a = \frac{1}{2}, h = - 12 and k = - 80$ .

Step by step solution

Step 1. Write down the given information.

The given equation is $y = \frac{1}{2} x^{2} + 12 x - 8$ .

Step 2. Calculation.

The given equation $y = \frac{1}{2} x^{2} + 12 x - 8$ is converted to standard form $y = a {(x - h)}^{2} + k$ as:

$\begin{matrix} y = \frac{1}{2} x^{2} + 12 x 鈭� 8 \\ = \frac{1}{2} (x^{2} + 24 x 鈭� 16) \\ = \frac{1}{2} (x^{2} + 24 x 鈭� 16 + {(12)}^{2} 鈭� {(12)}^{2}) .... (\begin{array}{l} Addand \\ subtract {(12)}^{2} \end{array}) \\ = \frac{1}{2} ((x^{2} + 24 x + {(12)}^{2}) 鈭� (16 + {(12)}^{2})) \\ = \frac{1}{2} {(x + 12)}^{2} 鈭� 80 \end{matrix}$

Here $a = \frac{1}{2}, h = - 12 and k = - 80$ .

Step 3. Conclusion.

The required form of the given equation is $y = \frac{1}{2} {(x + 12)}^{2} - 80$ where $a = \frac{1}{2}, h = - 12 and k = - 80$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Write the equation $y = \frac{1}{2} x^{2} + 12 x - 8$ in standard form.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Statistics

Logic and Functions

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Write the equation y=12x2+12x-8 in standard form.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Statistics

Logic and Functions

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write the equation $y = \frac{1}{2} x^{2} + 12 x - 8$ in standard form.