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2 years ago

Which of the following are characteristics of the graph of the quadratic parent function

Mathematics

2 answers:

Stolb23 [73]2 years ago

8 0

Answer:

D. It is U-shaped

Step-by-step explanation:

The standard form of a quadratic function is $y=a*x^{2} +b*x+c$ . The graph of quadratic function opens in the direction of the positive y-axis or negative y-axis, it depends on the coefficient of $x^{2}$ in the function. The shape of the graph of quadratic function is U shaped, because the greatest power of the x in the function is 2.

Hence The shape of quadratic function is U-shaped. It is the characteristics of the quadratic parent function.

Bogdan [553]2 years ago

4 0

It would be A. because it intercepts the x-axis and y-axis at (0, 0) and D. because it looks like a u

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2 years ago

Solve 5y'' + 3y' – 2y = 0, y(0) = 0, y'(O) = 2.8 y(t) =( Preview

Karolina [17]

Answer:

$y=\frac{4}{5}e^{t}-\frac{4}{5}e^{-\frac{2}{5}t}$

Step-by-step explanation:

The given equation 5y'' + 3y' - 2y =0 can be written as

$(5D^{2}+3D-2)y(t)=0$

Solving for complementary function we have Roots of $(5D^{2}+3D-2)$ as follows

$(5D^{2}+5D-2D-2)$

$5D(D+1)-2(D+1)=0\\\\(5D-2)(D+1)=0\\\\\therefore D=-1\\D=+2/5$

Thus the complementary function becomes

y= $y=c_{1}e^{m_{1}t}+c_{2}e^{m_{2}t}$

where

$m_{1},m_{2}$ are calculated roots

thus solution becomes

$y=c_{1}e^{-t}+c_{2}e^{\frac{2}{5}t}$

Now to solve for the coefficients we use the given boundary conditions

$y(0)=0\\\\\therefore c_{1}+c_{2}=0\\\\y'(0)=-c_{1}+\frac{2}{5}c_{2}=2.8\\\\\therefore c_{2}+\frac{2}{5}c_{2}=2.8\\\\c_{2}=2\\\\\therefore c_{1}=-2}$

hence the solution becomes

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2 years ago

How can I do this using

HACTEHA [7]

Answer:

See below.

Step-by-step explanation:

Part 1.

x + 12 <---------- Quotient.

------------------

x - 4 ( x^2 + 8x + 16

x^2- 4x

------------

12x + 16

12x - 48

----------

64 <--------- Remainder.

Part 2

f(4) = (4)^2 +8(4) + 16 = 16 + 32 + 16

= 64 Which is the remainder we found in the long division.

Part 3.

As you see in Parts 1 and 2, the Remainder Theorem tells you what the remainder is without doing the long division. If the remainder is 0 this means that the binomial you is a factor of the polynomial.

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3 years ago

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Naily [24]

Answer:

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Step-by-step explanation:

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2 years ago

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