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:

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

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

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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.

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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

Pure Maths

Decision Maths

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

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