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3 years ago

What is the equation in vertex

Mathematics

2 answers:

mote1985 [20]3 years ago

7 0

Hope this helps. Let me know if you have questions

jok3333 [9.3K]3 years ago

5 0

$\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{ope ns~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \stackrel{\textit{vertex}}{(3,-2)}~~ \begin{cases} h = 3\\ k = -2 \end{cases}\implies y=a(x-3)^2-2 \\\\\\ \stackrel{\textit{passes through}}{(5,-1)}~~ \begin{cases} x=5\\ y= -1 \end{cases}\implies -1=a(5-3)^2-2\implies 1=a(2)^2 \\\\\\ 1=4a\implies \cfrac{1}{4}=a~\hfill \boxed{y=\cfrac{1}{4}(x-3)^2-2}$

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The average value of a function f over the interval [−2,3] is −6 , and the average value of f over the interval [3,5] is 20. Wha

Xelga [282]

Answer:

The average value of $f$ over the interval $[-2,5]$ is $\frac{10}{7}$ .

Step-by-step explanation:

Let suppose that function $f$ is continuous and integrable in the given intervals, by integral definition of average we have that:

$\frac{1}{3-(-2)} \int\limits^{3}_{-2} {f(x)} \, dx = -6$ (1)

$\frac{1}{5-3} \int\limits^{5}_{3} {f(x)} \, dx = 20$ (2)

By Fundamental Theorems of Calculus we expand both expressions:

$\frac{F(3)-F(-2)}{3-(-2)} = -6$

$F(3) - F(-2) = -30$ (1b)

$\frac{F(5)-F(3)}{5-3} = 20$

$F(5) - F(3) = 40$ (2b)

We obtain the average value of $f$ over the interval $[-2, 5]$ by algebraic handling:

$F(5) - F(3) +[F(3)-F(-2)] = 40 + (-30)$

$F(5) - F(-2) = 10$

$\frac{F(5)-F(-2)}{5-(-2)} = \frac{10}{5-(-2)}$

$\bar f = \frac{10}{7}$

The average value of $f$ over the interval $[-2,5]$ is $\frac{10}{7}$ .

4 0

2 years ago

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damaskus [11]

A.
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3 0

2 years ago

Read 2 more answers

What is the solution for -10 < x - 9?

ikadub [295]

ANSWER:

x > - 1

STEP-BY-STEP EXPLANATION:

- 10 < x - 9

x - 9 > - 10

x > - 10 + 9

x > - 1

6 0

3 years ago

The price of patatoes first increased by 10% and then fell by 8%. Find the net percentage change in the price of patatoes.

timofeeve [1]

Answer:

10%-8%=2

2/8=0.25

0.25×100=25

The net percentage is 25%

6 0

2 years ago

Work out 3/5 of 900

Mars2501 [29]

Answer:

540

Step-by-step explanation:

1. We assume, that the number 900 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 900 is 100%, so we can write it down as 900=100%.

4. We know, that x is 3.5% of the output value, so we can write it down as x=3.5%.

5. Now we have two simple equations:

1) 900=100%

2) x=3.5%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

900/x=100%/3.5%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 3.5% of 900

900/x=100/3.5

(900/x)*x=(100/3.5)*x - we multiply both sides of the equation by x

900=28.571428571429*x - we divide both sides of the equation by (28.571428571429) to get x

900/28.571428571429=x

31.5=x

x=31.5

now we have:

3.5% of 900=31.5

3 0

3 years ago