Which linear equation represents the data given in the table?

Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo

mart [117]

Answer:

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Step-by-step explanation:

Given:

$y = -6x^2 + 3x + 2$

Required

Rewrite in vertex form

The vertex form of an equation is in form of: $y = a(x - h)^2+ k$

Solving: $y = -6x^2 + 3x + 2$

Subtract 2 from both sides

$y - 2 = -6x^2 + 3x + 2 - 2$

$y - 2 = -6x^2 + 3x$

Factorize expression on the right hand side by dividing through by the coefficient of x²

$y - 2 = -6(x^2 + \frac{3x}{-6})$

$y - 2 = -6(x^2 - \frac{3x}{6})$

$y - 2 = -6(x^2 - \frac{x}{2})$

Get a perfect square of coefficient of x; then add to both sides

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<em>Rough work</em>

The coefficient of x is $\frac{-1}{2}$

It's square is $(\frac{-1}{2})^2 = \frac{1}{4}$

Adding inside the bracket of $-6(x^2 - \frac{x}{2})$ to give: $-6(x^2 - \frac{x}{2} + \frac{1}{4})$

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: $-6(\frac{1}{4})$

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The expression becomes

$y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

Factorize the expression on the right hand side

$y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2$

$y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{7}{2})= -6(x - \frac{1}{2})^2$

$y +\frac{7}{2} = -6(x - \frac{1}{2})^2$

Make y the subject of formula

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

<em>Solved</em>

7 0

4 years ago

Read 2 more answers

The rectangular field has a perimeter of 98 meters. The width of the perimeter is three times as much as five times the length.

White raven [17]

Answer:

a) x = 3.0625m

y = 45.9375 m

b) A = 140.68359375 m²

Step-by-step explanation:

Let x be the length

Let y be the width

2x + 2y = 98

x + y = 49

y = 3(5x)

y = 15x

x + 15x = 49

16x = 49

x = 3.0625 m

y = 15(3.0625) = 45.9375

A = xy = 3.0625(45.9375) = 140.68359375

4 0

3 years ago

Will give Brainliest.

Oxana [17]

I believe the answers to be 75+5x=y

3 0

3 years ago

Read 2 more answers

Can someone help me please, thanks.

mars1129 [50]

Answer: 2.19 pounds

Step-by-step explanation:

35 / 16 is 2.1875, if you round that you get 2.19

6 0

3 years ago

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a restaurant served 6352 meals during one month. what statement correctly compares the value of the digit 6 in the number of mea

san4es73 [151]

6000+300 or a comma in between?

5 0

3 years ago