Q59. Write the equation聽y=-3x2-18x-1... [FREE SOLUTION]

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:

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

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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91影视

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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91影视

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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Mechanics Maths

Geometry

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

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