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3 years ago

the Function h(x)=1/2(x+3)^2+2. How is the graph of h(x) translated from the parent graph of a qaudratic function, f(x)=x^2

Mathematics

2 answers:

Kay [80]3 years ago

6 0

Answer:

Translation of h(x) is 2 unit down, 3 unit right and vertical stretch by 2

Step-by-step explanation:

Given function: $h(x)=\dfrac{1}{2}(x+3)^2+2$

Parent function: $f(x)=x^2$

It is parabolic function.

$h(x)=\dfrac{1}{2}(x+3)^2+2$

Shift 2 unit down

$g(x)=\dfrac{1}{2}(x+3)^2+2-2$

$g(x)=\dfrac{1}{2}(x+3)^2$

Shift 3 unit right

$g(x)=\dfrac{1}{2}(x+3-3)^2$

$g(x)=\dfrac{1}{2}x^2$

Vertical stretch by factor 2

$g(x)=2\cdot dfrac{1}{2}x^2$

$g(x)=x^2=f(x)$

So, Translation of h(x) is 2 unit down, 3 unit right and vertical stretch by 2

Tresset [83]3 years ago

3 0

Answer:

i'm not sure sorry

Step-by-step explanation:

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4 years ago

Consider F and C below. F(x, y, z) = y2 sin(z) i + 2xy sin(z) j + xy2 cos(z) k C: r(t) = t2 i + sin(t) j + t k, 0 ≤ t ≤ π (a) Fi

Liono4ka [1.6K]

Answer:

a) $f (x,y,z)= xy^2\sin(z)$

b) $\int_C F \cdot dr =0$

Step-by-step explanation:

Recall that given a function f(x,y,z) then $\nabla f = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})$ . To find f, we will assume it exists and then we will find its form by integration.

First assume that F = $\nabla f$ . This implies that

$\frac{\partial f}{\partial x} = y^2\sin(z)$ if we integrate with respect to x we get that

$f(x,y,z) = xy^2\sin(z) + g(y,z)$ for some function g(y,z). If we take the derivative of this equation with respect to y, we get

$\frac{\partial f}{\partial y} = 2xy\sin(z) + \frac{\partial g}{\partial y}$

This must be equal to the second component of F. Then

$2xy\sin(z) + \frac{\partial g}{\partial y}=2xy\sin(z)$

This implies that $\frac{\partial g}{\partial y}=0$ , which means that g depends on z only. So $f(x,y,z) = xy^2\sin(z) + g(z)$

Taking the derivative with respect to z and making it equal to the third component of F, we get

$xy^2\cos(z)+\frac{dg}{dz} = xy^2\cos(z)$

which implies that $\frac{dg}{dz}=0$ which means that g(z) = K, where K is a constant. So

$f (x,y,z)= xy^2\sin(z)$

b) To evaluate $\int_C F \cdot dr$ we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.

$\int_C F \cdot dr = f(r(\pi))-f(r(0))$

Recall that $r(\pi) = (\pi^2, 0, \pi)$ so $f(r(\pi)) = \pi^2\cdot 0 \cdot \sin(\pi) = 0$

Also $r(0) = (0, 0, 0)$ so $f(r(0)) = 0^2\cdot 0 \cdot \sin(0) = 0$

So $\int_C F \cdot dr =0$

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3 years ago

How do I simplify this? Include steps.<br> <img src="https://tex.z-dn.net/?f=%20%28%5Cfrac%7B5i%5E3t%5E4%7D%7B7%7D%29-2%20%20%20

navik [9.2K]

Simplify the following:
(5 i^3 t^4)/7 - 2
i^3 = i^2×i = (-1) i = -i:
(5×-i t^4)/7 - 2
Put each term in (5 (-i) t^4)/7 - 2 over the common denominator 7:
(5 (-i) t^4)/7 - 2 = (-5 i t^4)/7 - 14/7:
(-5 i t^4)/7 - 14/7
(-5 i t^4)/7 - 14/7 = (-5 i t^4 - 14)/7:
Answer: (-5 i t^4 - 14)/7

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3 years ago

Helppppp

sasho [114]

Answer:

186.5 + 2x

Step-by-step explanation:

First, radify 25. Luckily it's a perfect square so it will be 5.

Second, divide within the parentheses. You're expression should look like this.

(93-5+x+42/8)2

Divide 42/8. The decimal form would be 5.25, while the fraction should be 5 1/4.

Third, solve within the parentheses from left to right. Right now you're expression should look like this:

(93-5+x+5.25)2

Add all like terms

93-5+5.25=93.25

Fourth, multiply. Right now the expression should look like this:

(93.25 + x) 2

186.5 + 2x

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