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3 years ago

14

Is this answer correct on problem 3

2 answers:

Yuri [45]3 years ago

6 0

-1/4*x^2-x+3=-1/4*(x^2+4x)+3=-1/4*(x^2+4x+4)+4=-1/4*(x+2)^2+4
x0=-2

charle [14.2K]3 years ago

3 0

This is a vertical parabola which opens downwards

Use the formula

4p(y - k) = (x - h^2

converting to vertex form-
y =
-1/4(x^2 + 4x) + 3
y = -1/4[ (x + 2)^2] + 4

y - 4 = -1/4 (x + 2)^2

-4(y - 4) = (x + 2)^2 so the vertex is at (-2, 4)
comparing with the above formula
4p = -4
so p = -1 where p is the distance of the focus from the vertex
The vertex is at (-2,4) so the focus is at (-2, 4-1) = (-2, 3) Answer

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3 years ago

[30 POINTS] Please help!!!

Len [333]

Answer:

Part 1) $y=1.5x+5$

Part 2) $y=-(2/3)x-(11/3)$

Part 3) $y=0.25x+2.75$

Part 4) $y=-2x+5$

Part 5) $y=0.5x-1$

Part 6) The graph in the attached figure

Step-by-step explanation:

Part 1) we have

$m=3/2=1.5$

$point(-2,2)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-2=1.5(x+2)$

$y=1.5x+3+2$

$y=1.5x+5$

Part 2) we know that

If two lines are perpendicular

then

the product of their slopes is equal to minus one

so

$m1*m2=-1$

the slope of the line 1 is equal to

$m1=1.5$

Find the slope m2

$1.5*m2=-1$

$m2=-2/3$

Find the equation of the line 2

we have

$m2=-2/3$

$point(-7,1)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-1=(-2/3)(x+7)$

$y=-(2/3)x-(14/3)+1$

$y=-(2/3)x-(11/3)$

Part 3) we have

$m=1/4=0.25$

$point(1,3)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-3=0.25(x-1)$

$y=0.25x-0.25+3$

$y=0.25x+2.75$

Part 4) we have

$m=-2$

$b=5$ -----> y-intercept

we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

substitute the values

$y=-2x+5$

Part 5) we have that

The slope of the line 4 is equal to $-2$

so

the slope of the line perpendicular to the line 4 is equal to

$-2*m=-1\\m=(1/2)=0.5$

therefore

in this problem we have

$m=0.5$

$point(-2,-2)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y+2=0.5(x+2)$

$y=0.5x+1-2$

$y=0.5x-1$

Part 6)

using a graphing tool

see the attached figure

3 0

3 years ago