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3 years ago

Help please thank you!

Mathematics

1 answer:

monitta3 years ago

8 0

Answer:

• multiplied by 4p: (x -h)² +4pk = 0

• zeros for k > 0: none

• zeros for k = 0: one

• zeros for k < 0: two

Step-by-step explanation:

a) Multiplying by 4p removes the 1/(4p) factor from the squared term, but adds a factor of 4p to the k term. (It has no effect on the subsequent questions or answers, so we wonder why we're doing this.) The result is ...

(x -h)² +4pk = 0

b) The value of k is the vertical location of the vertex of the parabola with respect to the x-axis. The parabola opens upward, so for k > 0, the parabola does not cross the x-axis, and the number of real zeros is zero. (There are two complex zeros.)

c) As in part b, the value of k defines the vertex location. When it is zero, the vertex of the parabola is on the x-axis, so there is one real zero (It is considered to have multiplicity 2.)

d) As in part b, the value of k defines the vertex location. When it is negative, the vertex of the parabola is below the x-axis. Since the parabola opens upward, both branches will cross the x-axis, resulting in two real zeros.

_____

The attached graph shows a parabola with p=1/4 and h=2. The values shown for k are +1, 0, and -1. The coordinates of the real zeros are shown.

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If f and t are both even functions, is the product ft even? If f and t are both odd functions, is ft odd? What if f is even and

Natali5045456 [20]

Answer:

(a) If f and t are both even functions, product ft is even.

(b) If f and t are both odd functions, product ft is even.

Step-by-step explanation:

Even function: A function g(x) is called an even function if

$g(-x)=g(x)$

Odd function: A function g(x) is called an odd function if

$g(-x)=-g(x)$

(a)

Let f and t are both even functions, then

$f(-x)=f(x)$

$t(-x)=t(x)$

The product of both functions is

$ft(x)=f(x)t(x)$

$ft(-x)=f(-x)t(-x)$

$ft(-x)=f(x)t(x)$

$ft(-x)=ft(x)$

The function ft is even function.

(b)

Let f and t are both odd functions, then

$f(-x)=-f(x)$

$t(-x)=-t(x)$

The product of both functions is

$ft(x)=f(x)t(x)$

$ft(-x)=f(-x)t(-x)$

$ft(-x)=[-f(x)][-t(x)]$

$ft(-x)=ft(x)$

The function ft is even function.

(c)

Let f is even and t odd function, then

$f(-x)=f(x)$

$t(-x)=-t(x)$

The product of both functions is

$ft(x)=f(x)t(x)$

$ft(-x)=f(-x)t(-x)$

$ft(-x)=[f(x)][-t(x)]$

$ft(-x)=-ft(x)$

The function ft is odd function.

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Ganezh [65]

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Step-by-step explanation:

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