Rewrite the equation y^2 – 4y – 2x – 4 = 0 in standard form.

Mathematics

1 answer:

patriot [66]3 years ago

8 0

y² - 4y - 2x - 4 = 0

+2x +4 +2x + 4

y² - 4y = 2x + 4

+4 +4

(y - 2)² = 2x + 8

-8 -8

(y - 2)² - 8 = 2x

$\frac{(y - 2)^{2}}{2} - \frac{8}{2} = \frac{2x}{2}$

$\frac{1}{2}$ (y - 2)² - 4 = x

x = $\frac{1}{2}$ (y - 2)² - 4

Note: this is a parabola whose axis of symmetry is y = 2 and vertex is (-4, 2)

You might be interested in

What is a mathematical expression for x is fewer than 9?

Marianna [84]

The mathematical expression for x is is fewer than 9 is x< 9

3 0

2 years ago

Annalee hammered in nail into a piece of wood each time she hammer the nail it went to 1/8 Inch deeper into the word if she hamm

mash [69]

Answer: 0.5 inch

Step-by-step explanation:

Given

On hammering nail advances $\frac{1}{8}\ inch$ each time

Annalee hammered 4 times

So, total advancement of nail= $4\times \dfrac{1}{8}=\dfrac{1}{2}\ inch$

3 0

2 years ago

Please help... need help ASAP due today... which ones are the answers?

andrey2020 [161]

Answer:

Choices 1 and 4 are correct.

Step-by-step explanation:

We first need to find what the slope of the line is. That way, we can find out which possible answers are perpendicular to it:

$\frac{4-(-2)}{3-1}=\frac{6}{2}=3$

Since we now have the slope, we need the negative reciprocal of it. Remember: if x is the slope, it's negative reciprocal will be $-\frac{1}{x}$ . Therefore, if the line's slope is 3, then we need to find answers with a slope of $-\frac{1}{3}$ .

The first answer is correct, as you have marked. The second answer, while written a little weirdly, does show the slope as 3, which we know as wrong. The third choice is not correct, however. This equation is written in point-slope form, where $y-y_{1}=m(x-x_{1})$ . The only variable we have to worry about is m, which, in the third choice, is 3. The fourth answer is correct, which sounds weird at first. Let's put that equation into slope-intercept form: