Chapter 8: Q59. (page 416)

Write the equation $y = - 3 x^{2} - 18 x - 10$ in the form $y = a {(x - h)}^{2} + k$ .

Short Answer

Expert verified

The required form of the equation in $y = a {(x - h)}^{2} + k$ is $y = - 3 {(x + 3)}^{2} + 17$ where localid="1648620480283" $a = - 3, h = - 3 and k = 17$ .

Step by step solution

Step 1. Write down the given information.

The given equation is $y = - 3 x^{2} - 18 x - 10$ .

Step 2. Calculation.

The given equation $y = - 3 x^{2} - 18 x - 10$ is converted to $y = a {(x - h)}^{2} + k$ form as:

$\begin{matrix} y = - 3 x^{2} - 18 x - 10 \\ = - 3 (x^{2} + 6 x + \frac{10}{3}) \\ = - 3 (x^{2} + 6 x + \frac{10}{3} + {(3)}^{2} - {(3)}^{2}) .... (Addandsubtract {(3)}^{2}) \\ = - 3 (x^{2} + 6 x + {(3)}^{2} + (\frac{10}{3} - 9)) \\ = - 3 ({(x + 3)}^{2} - \frac{17}{3}) \\ = - 3 {(x + 3)}^{2} + 17 \end{matrix}$

Here localid="1648620544915" $a = - 3, h = - 3 and k = 17$ .

Step 3. Conclusion.

The required form of the given equation is $y = - 3 {(x + 3)}^{2} + 17$ where localid="1648620558780" $a = - 3, h = - 3 and k = 17$ .

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Write the equation $y = - 3 x^{2} - 18 x - 10$ in the form $y = a {(x - h)}^{2} + k$ .

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 equationy=-3x2-18x-10in the form y=ax-h2+k.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Logic and Functions

Pure Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Write the equation $y = - 3 x^{2} - 18 x - 10$ in the form $y = a {(x - h)}^{2} + k$ .