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3 years ago

7

A parabola passes through the points (-3,0), (-2,3), and (-1,4). What function does it represent? Use the graphing tool to deter

mine the function.
A.

f(x) = -x2 + x + 3

B.

f(x) = -2x2 − x + 3

C.

f(x) = -x2 − 2x + 3

D.

f(x) = 2x2 − x − 3

1 answer:

Stella [2.4K]3 years ago

8 0

Answer: C

Step-by-step explanation:

(-1,4) is the vertex. reflect (-2,3) and (-3,0) onto the other side of the y-axis. you may use desmos to plug in the functions and the answer will be C, since it goes through the points given and reflected.

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Make a conjecture of what the x-intercepts of the function<br> f(x) = (2x - 1)(x + 3) will be.

drek231 [11]

Answer:

x=-3,x1/2

Step-by-step explanation:

f(x)=(2x-1)(x+3)

TI find x intercept/zero substitute

f(x)=0

0=(2x-1)x(x+3)

swap the sides of the equation

(2x-1)x(x+3)=0

when the product of factors equals 0,at least one factor is zero

2x-1=0

x+3=0

solve the equation for x

x=1/2

x+3=0

solve the equation of x

x=-3

The equation has two solution

x=-3

x=1/2

3 0

3 years ago

For the function y=3x2: (a) Find the average rate of change of y with respect to x over the interval [3,6]. (b) Find the instant

nirvana33 [79]

Answer:

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

Step-by-step explanation:

a) Geometrically speaking, the average rate of change of $y$ with respect to $x$ over the interval by definition of secant line:

$r = \frac{y(b) -y(a)}{b-a}$ (1)

Where:

$a$ , $b$ - Lower and upper bounds of the interval.

$y(a)$ , $y(b)$ - Function exaluated at lower and upper bounds of the interval.

If we know that $y = 3\cdot x^{2}$ , $a = 3$ and $b = 6$ , then the average rate of change of $y$ with respect to $x$ over the interval is:

$r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}$

$r = 27$

The average rate of change of $y$ with respect to $x$ over the interval $[3,6]$ is 27.

b) The instantaneous rate of change can be determined by the following definition:

$y' = \lim_{h \to 0}\frac{y(x+h)-y(x)}{h}$ (2)

Where:

$h$ - Change rate.

$y(x)$ , $y(x+h)$ - Function evaluated at $x$ and $x+h$ .

If we know that $x = 3$ and $y = 3\cdot x^{2}$ , then the instantaneous rate of change of $y$ with respect to $x$ is:

$y' = \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}$

$y' = 6\cdot \lim_{h \to 0} x +3\cdot \lim_{h \to 0} h$

$y' = 6\cdot x$

$y' = 6\cdot (3)$

$y' = 18$

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

5 0

3 years ago

HELP PLEASE! I'm not sure what the right answer is.

jasenka [17]

I'm really not sure.
Sorry.

3 0

3 years ago

The perimeter of the blueprint is represented by the equation P=8x. What is the equation of the perimeter when solved for x

Korvikt [17]

Answer:

x = P/8

Step-by-step explanation:

The perimeter of the blueprint is given by the equation :

P = 8x

We need to solve the above equation for x.

Dividing both sides of the equation by 8.

$\dfrac{P}{8}=\dfrac{8x}{8}\\\\x=\dfrac{P}{8}$

Hence, the value of x is P/8

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3 years ago

21²/0.219 to 2 significant figures

Oksanka [162]

21^2/0.219 = 2013.69863
2 significant figures are the 20, so the answer is 2000

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2 years ago

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