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3 years ago

Write the equation of a parabola with vertex (2,-1) and directrix y=-3

Mathematics

1 answer:

tatuchka [14]3 years ago

7 0

Answer:

$y=-x^{2} -3x-3$

Step-by-step explanation:

a parabola is the graph of a quadratic equation, so the general equation is

$y=ax^{2} +bx+c$

If the directrix is negative, it means the graph opens down, so a is -

and c is -3

this gives us

$y=-x^{2} +bx-3$

all we need now is what is b

b is the y intercept for $y=mx+b$

to find the y intercept, we plug in 0 for x

$y=-x^{2} +bx-3\\y=-0^{2} +b(0)-3\\y=0+0-3\\y=-3$

so the y intercept is -3

so the equation is

$y=-x^{2} -3x-3$

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A2 = -8 and a5 = -512 Find a10

yawa3891 [41]

Answer:

The value of a₁₀ is -1352

Step-by-step explanation:

a₂ = -8

a₅ = -512

Now,

a₂ = -8 can be written as

a + d = -8 ...(1) and

a₅ = -512 can be written as

a + 4d = -512 ...(2)

Now, from equation (2) we get,

a + 4d = - 512

a + d + 3d = - 512

(-8) + 3d = - 512 (.°. a + d = -8)

3d = - 512 + 8

3d = - 504

d = - 504 ÷ 3

d = - 168

Now, for the value of a put the value of d = -168 in equation (1)

a + d = -8

a + (-168) = -8

a - 168 = -8

a = 168 - 8

a = 160

Now, For a₁₀

a₁₀ = a + 9d

a₁₀ = 160 + 9(-168)

a₁₀ = 160 - 1512

a₁₀ = -1352

Thus, The value of a₁₀ is -1352

-TheUnknownScientist

8 0

3 years ago

What is this ?????? plz helpppp

gogolik [260]

Answer:

The baker uses 15 cups of cereal for 10 cups of marshmallows

Step-by-step explanation:

The proportion 6:4 has to stay true in the answer, so both numbers have to be multiplied by the same number

6 x 2.5 = 15

4 x 2.5 = 15

both numbers were multiplied by the same number in this answer and it is the only answer that stays true to the ratio

6 0

3 years ago

A shoe store is offering a 25% discount on all pairs of shoes in the store. Every store employee gets an addtional 15% off the a

sergeinik [125]

The amount an employee has to pay for a pair of shoes, is $56, but there is no $56 option, so the only other answer it could be is C. $57

3 0

3 years ago

Enter the coefficients of the fifth Taylor polynomial T5(x) for the function f(x) = x5−3x4+2x2+5x−2 based at b=1. T5(x)= + (x−1)

DENIUS [597]

Compute the necessary values/derivatives of $f(x)$ at $x=1$ :

$f(1)=3$

$f'(1)=2$

$f''(1)=-12$

$f'''(1)=-12$

$f^{(4)}(1)=48$

$f^{(5)}(1)=120$

Taylor's theorem then says we can "approximate" (in quotes because the Taylor polynomial for a polynomial is another, exact polynomial) $f(x)$ at $x=1$ by

$T_5(x)=\dfrac3{0!}+\dfrac2{1!}(x-1)-\dfrac{12}{2!}(x-1)^2-\dfrac{12}{3!}(x-1)^3+\dfrac{48}{4!}(x-1)^4+\dfrac{120}{5!}(x-1)^5$

$T_5(x)=3+2(x-1)-6(x-1)^2-2(x-1)^3+2(x-1)^4+(x-1)^5$

###

Another way of doing this would be to solve for the coefficients $a,b,c,d,e,g$ in

$f(x)=a+b(x-1)+c(x-1)^2+d(x-1)^3+e(x-1)^4+g(x-1)^5$

by expanding the right hand side and matching up terms with the same power of $x$ .

5 0

3 years ago

Brainliest if correct

densk [106]

Answer:

u⁷

Step-by-step explanation:

When multiply variables with exponents , all you do is add the exponents

so,

our powers are 3,3,1 (because no exponent means to the power of 1)

Adding the powers is 7

so u⁷

6 0

2 years ago

Read 2 more answers