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4 years ago

Which function in vertex form is equivalent to f(x)=4+x^2-2x

Mathematics

1 answer:

morpeh [17]4 years ago

5 0

F(x)=4-2x+x^2
=4-1+1-x-x+x^2
=3+(1-x) - x(1-x)
= 3+(1-x) (1-x)
= 3 + (1 - x)^2
f(x) = (1 - x)^2 + 3

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How do I solve it because it’s really difficult

dybincka [34]

The solution of the equation is x= 3 and y = 2

Step-by-step explanation:

Given,

-3x-4y = -17 and

-x-3y = -9

The system of equation can be rewritten as

3x+4y = 17 ------eq 1 and

x+3y = 9 ------ eq 2

To solve for x and y

Multiplying eq 2 by 3 we get,

3x + 9y = 27

or, 3x = 27-9y

Putting this value of x into eq 1 we get,

27-9y +4y = 17

or, -5y = 17-27

or, -5y = -10

or, y = 2

Now put y=2 in eq 2 we get,

x = 9 - 3(2)

= 3

Hence the solution is x = 3 and y = 2

6 0

3 years ago

I can’t figure out how to use the zeros in the polynomial. Please explain

Temka [501]

Answer:

a) $P (x) = (x + 3) (x-1) (x-4)$

b) $P (x) = (2x + 5) (5x - 4) (x-6)$

c) $P (x) = (x-3) (x-1) (x-4) (x + 1) ^ 2$

Step-by-step explanation:

For the question a * you need to find a polynomial of degree 3 with zeros in -3, 1 and 4.

This means that the polynomial P(x) must be zero when x = -3, x = 1 and x = 4.

Then write the polynomial in factored form.

$P (x) = (x + 3) (x-1) (x-4)$

Note that this polynomial has degree 3 and is zero at x = -3, x = 1 and x = 4.

For question b, do the same procedure.

Degree: 3

Zeros: -5/2, 4/5, 6.

The factors are

$x = -\frac{5}{2}\\\\x +\frac{5}{2} = 0\\\\(2x +5) = 0$

---------------------------------------

$x =\frac{4}{5}\\\\x-\frac{4}{5} = 0\\\\(5x-4) = 0$

--------------------------------------

$x = 6\\\\(x-6) = 0$

--------------------------------------

$P (x) = (2x + 5) (5x - 4) (x-6)$

Finally for the question c we have

Degree: 5

Zeros: -3, 1, 4, -1

Multiplicity 2 in -1

$x = -3\\\\(x-3) = 0$

--------------------------------------

$x = 1\\\\(x-1) = 0$

--------------------------------------

$x = 4\\\\(x-4) = 0$

----------------------------------------

$x = -1\\\\(x + 1) = 0$

-----------------------------------------

$P (x) = (x-3) (x-1) (x-4) (x + 1) ^ 2$

8 0

3 years ago

Help I don't understand this question that well

Romashka-Z-Leto [24]

1st) You would find the volume of the larger solid. V = Base Area • Height = (10•15) • 10 = 1500
2nd find the volume of the smaller figure. (2•4) • 4 = 32
Subtract the first from second 1500 - 32 = 1468.
Then you have to find the area of the fsces left after you took out figure two and add them to the total. 4•2 = 8. 4•2 = 8. 4•4 = 16
1462 + 16 + 8 + 8 = 1494 inches cubed

3 0

3 years ago

Evaluate the expression

PolarNik [594]

$\frac{16^{6/4}}{16^{2/2} }$