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2 years ago

FREE 50+ POINTS GET YOUR DOUGH HERE

Mathematics

2 answers:

Vaselesa [24]2 years ago

7 0

Answer:

Thanks for the points!!!!!!

goldfiish [28.3K]2 years ago

7 0

Answer:

H u h

Step-by-step explanation:

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What would y=x^2 +x+ 2 be in vertex form

balu736 [363]

Answer:

$y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

Step-by-step explanation:

$y = {x}^{2} + x + 2$

We can covert the standard form into the vertex form by either using the formula, completing the square or with calculus.

$y = a(x - h)^{2} + k$

The following equation above is the vertex form of Quadratic Function.

Vertex — Formula

$h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a}$

We substitute the value of these terms from the standard form.

$y = a {x}^{2} + bx + c$

$h = - \frac{1}{2(1)} \\ h = - \frac{ 1}{2}$

Our h is - 1/2

$k = \frac{4(1)(2) - ( {1})^{2} }{4(1)} \\ k = \frac{8 - 1}{4} \\ k = \frac{7}{4}$

Our k is 7/4.

Vertex — Calculus

We can use differential or derivative to find the vertex as well.

$f(x) = a {x}^{n}$

Therefore our derivative of f(x) —

$f'(x) = n \times a {x}^{n - 1}$

From the standard form of the given equation.

$y = {x}^{2} + x + 2$

Differentiate the following equation. We can use the dy/dx symbol instead of f'(x) or y'

$f'(x) = (2 \times 1 {x}^{2 - 1} ) + (1 \times {x}^{1 - 1} ) + 0$

Any constants that are differentiated will automatically become 0.

$f'(x) = 2 {x}+ 1$

Then we substitute f'(x) = 0

$0 =2x + 1 \\ 2x + 1 = 0 \\ 2x = - 1 \\x = - \frac{1}{2}$

Because x = h. Therefore, h = - 1/2

Then substitute x = -1/2 in the function (not differentiated function)

$y = {x}^{2} + x + 2$

$y = ( - \frac{1}{2} )^{2} + ( - \frac{1}{2} ) + 2 \\ y = \frac{1}{4} - \frac{1}{2} + 2 \\ y = \frac{1}{4} - \frac{2}{4} + \frac{8}{4} \\ y = \frac{7}{4}$

Because y = k. Our k is 7/4.

From the vertex form, our vertex is at (h,k)

Therefore, substitute h = -1/2 and k = 7/4 in the equation.

$y = a {(x - h)}^{2} + k \\ y = (x - ( - \frac{1}{2} ))^{2} + \frac{7}{4} \\ y = (x + \frac{1}{2} )^{2} + \frac{7}{4}$

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2 years ago

If you spend $448.37 on a car each month, what is your new subtotal of take-home pay after expenses? $480.29 $629.75 $779.21 $92

Black_prince [1.1K]

I just had the question and the answer is $629.75

8 0

2 years ago

Read 2 more answers

Which linear inequality is represented by the graph?

mixer [17]

Answer: 3

Step-by-step explanation:

6 0

1 year ago

X + y = 4 x - y = 6 consistent, inconsistent, equivalent

Ad libitum [116K]

Inconsistent maybe???

6 0

2 years ago

Use the net to find the surface area of the prism 8in 15in 17in 9in

exis [7]

Answer:

The surface area of the prism is 480 in².

Step-by-step explanation:

Given:

The prism dimensions are 8in 15in 17in and 9in.

Now, to find the surface area:

So, to get the surface area we put formula:

a=8in, b=15in, c=17in and h=9in.

Surface area = 2A+(a+b+c)h.

Whereas, $A=\sqrt{s(s-a)(s-b)(s-c)}$

And, $s=\frac{a+b+c}{2}$

Now, we find s first:

$s=\frac{a+b+c}{2}$

$s=\frac{8+15+17}{2}$

$s=\frac{40}{2}=20.$

Then, we get A :

$A=\sqrt{s(s-a)(s-b)(s-c)}$

$A=\sqrt{20(20-8)(20-15)(20-17)}$

$A=\sqrt{20(12)(5)(3)}$

On solving we get:

$A=\sqrt{3600}=60.$

Now, putting the value of A in the formula to get the surface area:

$Surface area = 2A+(a+b+c)h.$

$Surface area = 2\times 60+(8+15+17)9.$

$Surface area = 120+(40)9.$

$Surface area = 120+360.$

$Surface area = 480\ in^2.$

Therefore, the surface area of the prism is 480 in².

6 0

2 years ago