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Stolb23 [73]
3 years ago
15

the standard for of the equation of a parabola is y=x^2+4x+11. What is the vertex for of the equation?

Mathematics
1 answer:
Eva8 [605]3 years ago
6 0
Convert to vertex form

or easier
for y=ax²+bx+c
the x value of the vertex is \frac{-b}{2a}
and the y value is found by subsituting the x value in for x

so
y=1x²+4x+11
a=1
b=4

the x value of the vertex is \frac{-4}{2(1)}=\frac{-4}{2}=-2

the y value is found by subsituting -2 for x
y=(-2)²+4(-2)+11
y=4-8+11
y=7

the vertex is (-2,7)
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Please help! These mathematics are very confusing. need help right away.
Ostrovityanka [42]
<span>
Exercise #1:
Point H = (–2, 2)
Point J = (–2, –3)
Point K = (3, –3)

It would be very helpful if you could take a pencil and a piece
of paper, and sketch a graph with these points on it.  Then
you'd immediately see what's going on.

Notice that points H and J have the same x-coordinate, but
different y-coordinates, so they're on the same vertical line.

</span><span>Notice that points J and K have different x-coordinates but
the same y-coordinate, so they're on the same horizontal line.

Notice that point-J is on both the horizontal line and the vertical
line, so the lines meet there, and they're perpendicular.
Point-J is one corner of the square.

H is another corner of the square.  It's 5 units above J.

K is another corner of the square.  It's 5 units to the right of J.

The fourth corner is (2, 3) ... 5 to the right of H,
                                       and 5 above K.
____________________________________

Exercise #2:
</span><span>Point H = (6, 2)
Point J = (–2, –4)
Point K = (-2, y) .

</span><span>It would be very helpful if you could take a pencil and a piece
of paper, and sketch a graph with these points on it.  Then
you'd immediately see what's going on.

</span><span>Notice that points J and K have the same x-coordinate, but
different y-coordinates, so they're on the same vertical line.

We need K to connect to point-H in such a way that it's on
the same horizontal line as H.  Then the vertical and horizontal
lines that meet at K will be perpendicular, and we'll have the
right angle that we need there to make the right triangle.
So K and H need to have the same y-coordinate.
H is the point (6, 2).  So K has to be up at  (2, 2) .
____________________________________________

Exercise #3:
</span>
<span>Point H = (-6, 2)
Point J = (–6, –1)
Point K = (4, 2) .
</span>
<span>It would be very helpful if you could take a pencil and a piece
of paper, and sketch a graph with these points on it.  Then
you'd immediately see what's going on.

This exercise is exactly the same as #1, except that it's a
rectangle instead of a square.  It's still make of horizontal
and vertical lines, and that's all we need to know in order
to solve it.</span><span>

Notice that points H and J have the same x-coordinate, but
different y-coordinates, so they're on the same vertical line.

</span><span>Notice that points H and K have different x-coordinates but
the same y-coordinate, so they're on the same horizontal line.

Notice that point-H is on both the horizontal line and the vertical
line, so the lines meet there, and they're perpendicular.
Point-H is one corner of the rectangle.

J is another corner of the rectangle.  It's 3 units below H.

K is another corner of the square.  It's 4 units to the right of H.

The fourth corner is (2, -1) ... 4 to the right of J,
                                       and  3 below K.

</span>
5 0
3 years ago
Cocoa plant type 1 yielded 155 bushels per acre last year at a research farm. This year,
ankoles [38]

Answer:confounding variable

Step-by-step explanation:

7 0
3 years ago
Limitation of -4 to the left of the absolute value of x+4 divided by x+4
timama [110]

I believe you're asking about the one-sided limit,

\displaystyle \lim_{x\to-4^-}\frac{|x+4|}{x+4}

Recall the definition of absolute value:

• |x| = x if x\ge0

• |x| = -x if x < 0

Since we're approaching -4 from the left, we're effectively focusing on a domain of x or x+4. So, by the definition above, we have |x+4| = -(x+4). Then in the limit, we have

\displaystyle \lim_{x\to-4^-}\frac{|x+4|}{x+4} = \lim_{x\to-4^-}\frac{-(x+4)}{x+4} = \lim_{x\to-4^-}(-1) = \boxed{-1}

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3 years ago
Which phrase accurately describes a distribution that's bell-shaped but not symmetric?
Evgen [1.6K]
What is symetertic to help
7 0
3 years ago
(100 – 40)/2 - 30 =?
Lena [83]
=(100-40)/2-30 =60/2-30 =30-30 =0
4 0
4 years ago
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