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Suppose that equation of parabola is
y =ax² + bx + c

Since parabola passes through the point (2,−15) then
−15 = 4a + 2b + c

Since parabola passes through the point (-5,-29), then
−29 = 25a − 5b + c

Since parabola passes through the point (−3,−5), then
−5 = 9a − 3b + c

Thus, we obtained following system:
4a + 2b + c = −15
25a − 5b + c = −29
9a − 3b + c = −5

Solving it we get that
a = −2, b = −4, c = 1

Thus, equation of parabola is
y = −2x²− 4x + 1

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Rewriting in the form of
(x - h)² = 4p(y - k)

i) -2x² - 4x + 1 = y

ii) -3x² - 7x = y - 11
(-3x² and -7x are isolated)

iii) -3x² - 7x - 49/36 = y - 1 - 49/36
(Adding -49/36 to both sides to get perfect square on LHS)

iv) -3(x² + 7/3x + 49/36) = y - 3
(Taking out -3 common from LHS)

v) -3(x + 7/6)² = y - 445/36

vi) (x + 7/6)² = -⅓(y - 445/36)
(Shifting -⅓ to RHS)

vii) (x + 1)² = 4(-1/12)(y - 445/36)
(Rewriting in the form of 4(-1/12) ; This is 4p)

So, after rewriting the equation would be -

(x + 7/6)² = 4(-⅛)(y - 445/36)

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I hope this is what you wanted.

Regards,
Divyanka♪
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6 0

3 years ago

Read 2 more answers

4380 rounded to the nearest 100

maks197457 [2]

4,400

The number 3 is in the hundredths place the 8 is behind the 3 so it’s larger than 5 so you turn the 3 into a 4(4,400) and turn all the numbers behind zero (4,400).

4 0

3 years ago

Read 2 more answers

This figure is made up of a rectangle and parallelogram.

ivann1987 [24]

The area of the figure is 40 units. (rounded off from 39.998 units)

Step-by-step explanation:

1. Area of the figure = Area of Rectangle + Area of Parallelogram.

2. Naming points:

Let the rectangle consist of points A(-6,-1), B(-5,-5), C(3,-3) and D(2,1).

Let the parallelogram consist of points C(3,-3), D(2,1), E(2,7) and F(3,3).

3. Each coordinate has a point on the x-axis and a point on the y-axis. We shall refer to these points as x', x'' ,x''' and so on corresponding to the x-axis values of A, B, C and so on in that order till F. For the y-axis points, we will name them in the series of y', y'', y''' and so on.

In simple words, in A(-6,1), x' = -6; y' = -1

4. Formula for finding area:

Area of a rectangle = length (l) × width (w)

Area of a parallelogram = base (b) x height (h)

5. Finding area of the rectangle:

l = AD = $\sqrt{[x'''' - x']^{2} - [y'''' - y']^{2}}$

, i.e. AD = $\sqrt{[2 - (-6)]^{2} - [1 - (-1)]^{2}}$

, i.e. AD = √68 = 8.246 (rounded to 3 decimals) = l

Now, w = AB = $\sqrt{[x'' - x']^{2} - [y'' - y']^{2}}$

, i.e. AB = $\sqrt{[(-5) - (-6)]^{2} - [(-5) - (-1)]^{2}}$

, i.e. AB = √17 = 4.123 (rounded to 3 decimals) = w

Area of rectangle = l x w = 8.246 x 4.123 = 33.998 units.

6. Finding area of the parallelogram:

b = DE = 6 units (we can observe this from the graph, i.e. points from 1 to 7 on the y axis)

h = Height is the line drawn perpendicular to the base from point F, which as we can see is 1 unit long.

Hence, Area of parallelogram = b x h = 6 x 1 = 6 units.

7. Now, adding both, we can arrive at the final answer.

Area of the figure = Area of rectangle + Area of parallelogram,

i.e. 33.998 units + 6 units = 39.998 units. (can be rounded off to 40 units)

4 0

3 years ago