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3 years ago

Find the vertex of y = x^2 – 2x – 15

Mathematics

2 answers:

svet-max [94.6K]3 years ago

7 0

The vertex is ( 1, -16 ).

solong [7]3 years ago

7 0

Answer:

The vertex is at (h, k), which here is (1, -16).

Step-by-step explanation:

One of the quicker ways to approach this proplem is to "complete the square," which puts the equation into "vertex form."

Starting with y = x^2 – 2x – 15, add 1 to, and then subtract 1 from, x^2 – 2x :

y = x^2 – 2x + 1 - 1– 15

Now re-write x^2 – 2x as (x - 1)^2 - 1:

y = (x - 1)^2 - 1 – 15. or y = (x - 1)^2 - 16, which has the form y = (x - h)^2 + k. Comparing these two equations, we see that h = 1 and k = -16.

The vertex is at (h, k), which here is (1, -16).

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2 years ago

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3 years ago

Solve the initial value problem y'=2 cos 2x/(3+2y),y(0)=−1 and determine where the solution attains its maximum value.

zloy xaker [14]

Answer:

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Step-by-step explanation:

We are given that

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y(0)=-1

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Taking integration on both sides then we get

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Using formula

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Substitute x=0 and y=-1

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Substitute the value of C

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$y^2+3y-sin 2x+2=0$

$y=\frac{-3\pm\sqrt{(3)^2-4(1)(-sin2x+2)}}{2}$

By using quadratic formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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Hence, the solution $y=\frac{-3\pm\sqrt{4sin2x+1}}{2}$

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3 years ago

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Vaselesa [24]

Answer:

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Step-by-step explanation:

#Adults tickets = A

#Students tickets = S

A + S = 150

5A (means the price is $5 times the number of Adult tickets) equals the total amount for all of the Adult tickets altogether

3S (means the price is $3 times the number of Student tickets) equals the total amount for all of the students tickets altogether

5A + 3S = 610 (Means adding the total of all the student tickets plus adult tickets will equal $610 for all tickets sold)

Using both equations now, you can use substitution or elimination to solve for one of the variables. Then you can use the variable to substitute to solve the remaining one.

A + S = 150

5A + 3S = 610

Substitution:

A = 150 - S (Rearrange the first equation by moving S to the other side)

Substitute into the other equation

5 (150 - S) + 3S = 610

750 - 5S + 3S = 610 Combine like terms : -2S = -140

Solve for S = 70

Substitute into A + S = 150 A + (70) = 150

A = 80

3 0

3 years ago