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13 days ago

Which equation is y = 6x2 + 12x – 10 rewritten in vertex form?

Mathematics

2 answers:

Inessa [3.9K]13 days ago

7 0

Answer:

$y=6(x+1)^{2}-16$

Detailed steps:

Begin with the standard form you already know

The vertex form for a vertical parabola can be written as

$y=a(x-h)^{2}+k$

and

(h,k) denotes the parabola's vertex

For this example the given equation is

$y=6x^{2}+12x-10$

To convert it into vertex form:

Collect like terms in x and move the constant to the other side

$y+10=6x^{2}+12x$

Next, factor the leading coefficient from the x-terms

$y+10=6(x^{2}+2x)$

Complete the square; be sure to add the same quantity to both sides so the equality holds

$y+10+6=6(x^{2}+2x+1)$

$y+16=6(x^{2}+2x+1)$

Now express the result as a perfect square trinomial

$y+16=6(x+1)^{2}$

$y=6(x+1)^{2}-16$ —→ this is the equation in vertex form

The vertex is the point $(-1,-16)$

lawyer [4K]13 days ago

5 0

Y = 6 x² + 12 x - 10. Factor out the 6 to get 6 ( x² + 2 x ) - 10. Rewrite the quadratic by adding and subtracting 1 inside the parentheses: 6 ( ( x² + 2 x + 1 ) - 1 ) - 10.
This reduces to 6 ( x + 1 )² - 6 - 10 = 6 ( x + 1 )² - 16 ( vertex form)

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The solution is 20 days, found as follows:
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15 days ago

LMN is a straight angle. Find m LMP and m NMP

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3 0

9 days ago

A customer/member owes $10.51 and pays $50.00 in cash. The change due is $39.49. Provide the amount owed using the smallest numb

Leona [4187]

The total number of bills and coins is 14.

Step-by-step explanation:

To minimize the count of bills and coins, start with the largest denominations that fit within the amount.

The change due is $39.49.

Start with:

-$20 bill (largest under $39.49)

Remaining: $19.49

-$10 bill (largest under $19.49)

Remaining: $9.49

-$5 bill (largest under $9.49)

Remaining: $4.49

Then:

4 × $1 bills (to cover $4.49)

Remaining: $0.49

-$0.25 coin (quarter)

Remaining: $0.24

2 × $0.10 coins (dimes)

Remaining: $0.04

4 × $0.01 coins (pennies)

The final composition includes:

1 twenty-dollar bill

1 ten-dollar bill

1 five-dollar bill

4 one-dollar bills

1 quarter

2 dimes

4 pennies

Totaling 14 pieces.

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17 days ago