Find the Vertex -x^2-6x+4

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Algebra

$- x^{2} - 6 x + 4$

Set the polynomial equal to $y$ to find the properties of the parabola.

$y = - x^{2} - 6 x + 4$

Rewrite the equation in vertex form.

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Complete the square for $- x^{2} - 6 x + 4$ .

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Use the form $a x^{2} + b x + c$ , to find the values of $a$ , $b$ , and $c$ .

$a = - 1, b = - 6, c = 4$

Consider the vertex form of a parabola.

$a {(x + d)}^{2} + e$

Substitute the values of $a$ and $b$ into the formula $d = \frac{b}{2 a}$ .

$d = - \frac{6}{2 (- 1)}$

Simplify the right side.

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Cancel the common factor of $6$ and $2$ .

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Factor $2$ out of $6$ .

$d = - \frac{2 \cdot 3}{2 \cdot - 1}$

Move the negative one from the denominator of $\frac{3}{- 1}$ .

$d = - (- 1 \cdot 3)$

Multiply.

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Multiply $- 1$ by $3$ .

$d = 3$

Multiply $- 1$ by $- 3$ .

$d = 3$

Find the value of $e$ using the formula $e = c - \frac{b^{2}}{4 a}$ .

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Simplify each term.

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Raise $- 6$ to the power of $2$ .

$e = 4 - \frac{36}{4 \cdot - 1}$

Multiply $4$ by $- 1$ .

$e = 4 - \frac{36}{- 4}$

Divide $36$ by $- 4$ .

$e = 4 + 9$

Multiply $- 1$ by $- 9$ .

$e = 4 + 9$

Add $4$ and $9$ .

$e = 13$

Substitute the values of $a$ , $d$ , and $e$ into the vertex form $a {(x + d)}^{2} + e$ .

$- {(x + 3)}^{2} + 13$

Set $y$ equal to the new right side.

$y = - {(x + 3)}^{2} + 13$

Use the vertex form, $y = a {(x - h)}^{2} + k$ , to determine the values of $a$ , $h$ , and $k$ .

$a = - 1$

$h = - 3$

$k = 13$

Find the vertex $(h, k)$ .

$(- 3, 13)$

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Name

Name	one billion three hundred twenty-five million eight hundred thirty-one thousand eight hundred sixty-eight

Interesting facts

1325831868 has 128 divisors, whose sum is 7076892672
The reverse of 1325831868 is 8681385231
Previous prime number is 8627

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 45
Digital Root 9

Name

Name	one billion three hundred eighty-three million five hundred seventy-five thousand five hundred twenty-eight

Interesting facts

1383575528 has 32 divisors, whose sum is 4672781568
The reverse of 1383575528 is 8255753831
Previous prime number is 1471

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 47
Digital Root 2

Name

Name	six hundred forty-seven million twelve thousand six hundred seventy-three

Interesting facts

647012673 has 32 divisors, whose sum is 803152800
The reverse of 647012673 is 376210746
Previous prime number is 37

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 36
Digital Root 9

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