Chapter 8: Q57. (page 416)

Write the equation $y = 3 x^{2} - 6 x + 5$ in the form $y = a {(x - h)}^{2} + k y = a {(x - h)}^{2} + k$ .

Short Answer

Expert verified

The required form of the equation in $y = a {(x - h)}^{2} + k$ is $y = 3 {(x - 1)}^{2} + 2$ where $a = 3, h = 1 and k = 2$ .

Step by step solution

Step 1. Write down the given information.

The given equation is $y = 3 x^{2} - 6 x + 5$ .

Step 2. Calculation.

The given equation $y = 3 x^{2} - 6 x + 5$ is converted to $y = a {(x - h)}^{2} + k$ form as:

\begin{matrix} y = 3 x^{2} - 6 x + 5 \\ = 3 (x^{2} - 2 x + \frac{5}{3}) \\ = 3 (x^{2} - 2 x + \frac{5}{3} + {(- 1)}^{2} - {(- 1)}^{2}) .... (Addandsubtract {(- 1)}^{2}) \\ = 3 ((x^{2} - 2 x + {(- 1)}^{2}) + (\frac{5}{3} - 1)) \\ = 3 ({(x - 1)}^{2} + \frac{2}{3}) \\ = 3 {(x - 1)}^{2} + 2 \end{matrix}

Here $a = 3, h = 1 and k = 2$ .

Step 3. Conclusion.

The required form of the given equation is $y = 3 {(x - 1)}^{2} + 2$ where $a = 3, h = 1 and k = 2$ .

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Write the equation $y = 3 x^{2} - 6 x + 5$ in the form $y = a {(x - h)}^{2} + k y = a {(x - h)}^{2} + k$ .

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=3x2-6x+5 in the formy=ax-h2+ky=ax-h2+k.

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

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Write the equation $y = 3 x^{2} - 6 x + 5$ in the form $y = a {(x - h)}^{2} + k y = a {(x - h)}^{2} + k$ .