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2 years ago

If the graph of the following parabola is shifted two units left and three units down, what is the resulting equation?

Mathematics

1 answer:

mafiozo [28]2 years ago

7 0

Answer:

$x=-8\left(y+3\right)^2-2$

Step-by-step explanation:

Because the x and y have been reversed in this equation, shifting the parabola to the left will be outside of the exponent and shifting up and down will be inside with the exponent.

The equation becomes $x=-8\left(y+3\right)^2-2$ .

Where subtracting by 2 moves it two units to the left and adding by 3 moves it 3 units down.

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Find all the zeros of the equation x^4-6x^2-7x-6=0

rusak2 [61]

Answer:

The zeros are

$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Step-by-step explanation:

We have been given the equation x^4-6x^2-7x-6=0

Use rational root theorem, we have

$a_0=6,\:\quad a_n=1$

$\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:6,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1$

$\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:3,\:6}{1}$

$-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2$

$=\left(x+2\right)\frac{x^4-6x^2-7x-6}{x+2}\\$

$=x^3-2x^2-2x-3$

Again factor using the rational root test, we get

$=\left(x+2\right)\left(x-3\right)\left(x^2+x+1\right)$

Using the zero product rule, we have

$x+2=0:\quad x=-2\\x-3=0:\quad x=3\\x^2+x+1=0\\\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\\\=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

Therefore, the zeros are

$x=-2,\:x=3,\:x=-\frac{1}{2}+i\frac{\sqrt{3}}{2},\:x=-\frac{1}{2}-i\frac{\sqrt{3}}{2}$

4 0

2 years ago

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A rectangle has two side lengths of 8 inches and two side lengths of 10 inches. What is the perimeter of the rectangle?

Ronch [10]

The perimeter is 36
8+8=16
10+10=20
20+16=36

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2 years ago

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Find the slope of (0,0) (6,8)

lara31 [8.8K]

Answer:

8/6 or 4/3

Step-by-step explanation:

Rise divided by run. Rise is difference in y values. 8-0=8

Run is difference in x values 6-0=6

Divide 8/6 then simplify. 4/3

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2 years ago

Can someone please help me with this .

schepotkina [342]

- 3x + 4y = - 11
y = 2x - 4

-3x + 4(2x - 4) = -11
-3x + 8x - 16 = - 11
5x = -11 + 16
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x = 5/5
x = 1

y = 2x - 4
y = 2(1) - 4
y = 2 - 4
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Solution: (1, -2)

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GuDViN [60]

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