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1 year ago

X2 - 4x + 4 = 0 solve following quadratic equations graphically and a table

1 answer:

6 0

Let's create a table, and use arbitrary values of x between -3 and 3 (if the solution is not in this interval, we can use another one later). If we call:

$f(x)=x^2-4x+4$

We want to find the x's for with f(x) = 0

This is the table:

And now we can evaluate f(x) in each value of x to complete the table:

$\begin{gathered} f(-3)=(-3)^2-4\cdot(-3)+4=9+12+4=25 \\ f(-2)=(-2)^2-4\cdot(-2)+4=4+8+4=16 \\ f(-1)=(-1)^2-4\cdot(-1)+4=1+4+4=9 \\ f(0)=0^2-4\cdot0+4=4 \\ f(1)=1^2-4\cdot1+4=1-4+4=1 \\ f(2)=2^2-4\cdot2+4=4-8+4=0 \\ f(3)=3^2-4\cdot3+4=9-12+4=1 \end{gathered}$

The table is:

If we use this values and plot them in the cartesian plane.

We get:

And now if we plot a line that connects the points, we get the graph of the quadratic equation:

Since the problem ask us to find the value of x for which f(x) = 0, we can see both in the table and in the graph that this value is x = 2

You might be interested in

Determine the 1-unit growth factor for f f. [We encourage you to write the expression that represents the value of the growth fa

timofeeve [1]

Answer: The complete question is found in the attachment

Step-by-step explanation:

a) To determine the 1-unit growth factor for f

= 2.1/1.75 = 1.2

b) To determine the 1-unit percent change for f

=100 x 1-1.2/1 = 0.2 x 100= 20%

c) to determine the initial value of f

f(x)= abˣ , b =1.2 a=initial value

at (-1,2.1)

2.1= (1.2)⁻¹ x a

a = 2.1/(1.2)⁻¹

a = 2.1 x 1.2 = 2.52

d) to determine the function formula for f

f(x)= abˣ = 2.52(1.2)ˣ

6 0

3 years ago

Which number is less then -2<45 but grater then -3<15?

stepan [7]

Answer:

Step-by-step explanation:

3 0

3 years ago

A company selling light bulbs claims in its advertisements that its light bulbs’ average life is 1000 hours. In fact, the life s

tamaranim1 [39]

Answer:

15.87%

Step-by-step explanation:

Given that:

The mean (μ) = 1000 hours, the standard deviation (σ) = 100 hours.

The z score provides a means of measurement in statistics to determine the variation of a raw score from the mean. The z score is given as:

$z=\frac{x-\mu}{\sigma}$

To find that a randomly chosen light bulb will last less than 900 hours:

$z=\frac{x-\mu}{\sigma}=\frac{9000-1000}{100}=-1$

Therefore, P(x < 900) = P(z < -1) = 0.1587 = 15.87%

7 0

3 years ago

A 0.45-mm-wide slit is illuminated by light of wavelength 590 nm. What is the width (in mm) of the central maximum on a screen 1

Hitman42 [59]

Answer:

$w = \frac{2(590x10^{-9}) (1.5m)}{0.45x10^{-3}}=3.93 x10^{-3} m$

And if we convert this into mm we got:

$w= 3.93 x10^{-3} m *\frac{1000mm}{1 m}= 3.93 mm$

Step-by-step explanation:

For this case we have the following info givenL

$\lambda = 590 nm = 590 x10^{-9}m$ represent the wavelength

$s = 0.45 mm *\frac{1m}{1000 mm}= 0.45x10^{-3} m$ represent the width of the single slit

$L = 1.5 m$ represent the longitude

And we want to find the maximum width of the central maximum in mm, so we can use the following formula:

$w s = 2 \lambda L$

And if we solve for w the width we got:

$w = \frac{2\lambda L}{s}$

And replacing we got:

$w = \frac{2(590x10^{-9}) (1.5m)}{0.45x10^{-3}}=3.93 x10^{-3} m$

And if we convert this into mm we got:

$w= 3.93 x10^{-3} m *\frac{1000mm}{1 m}= 3.93 mm$

6 0

3 years ago

What equation represent s "a number y decreased by 25 is 100

Aleksandr [31]

"A number y" basically means the variable y. "Decreased by" means minus. "Is" means equals. So: y minus 25 equals 100.

This should be pretty easy to convert into an equation: y-25=100.

8 0

3 years ago