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2 years ago

What is 3/8x-12+-6 ?

Mathematics

1 answer:

Cloud [144]2 years ago

6 0

Answer:

-10.5 is 3/8x-12+-6 answer

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Please Help! 30 POINTS! Given the following three points, find by hand the quadratic function they represent. (−1,−8), (0,−1),(1

ycow [4]

Answer:

(1) B

(2) D

Step-by-step explanation:

(1)

Let the quadratic function be:

$y = ax^{2} + bx + c$

For the point, (0,-1),

$y = ax^{2} + bx + c$

$-1=(a\times0)+(b\times0}+c\\-1=c\\c=-1$

Then the equation is:

$y = ax^{2} + bx -1$

For the point (-1, -8) ,

$y = ax^{2} + bx -1$

$-8=(a\times (-1)^{2})+(b\times -1)-1\\-8=a-b-1\\a-b=-7...(i)$

For the point (1, 2) ,

$y = ax^{2} + bx -1$

$2=(a\times (1)^{2})+(b\times 1)-1\\2=a+b-1\\a+b=3...(ii)$

Add the two equations and solve for a as follows:

$a-b=-7\\a+b=3\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\2a = -4\\a = -2$

Substitute a = -2 in (i) and solve for b as follows:

$a-b=-7\\-2-b=-7\\b=5$

Thus, the quadratic function is:

$f(x)=-2x^{2}+5x-1$

The correct option is (b).

(2)

The ordered pairs are:

(5, 7), (7, 11), (9, 14), (11, 18)

Represent them in an XY table as follows:

X : 5 | 7 | 9 | 11

Y : 7 | 11 | 14 | 18

Compute the difference between the Y values as follows:

Diff = 11 - 7 = 4

Diff = 14 - 11 = 3

Diff = 18 - 14 = 4

Now compute the difference between the Diff values:

d = 3 - 4 = -1

d = 4 - 3 = 1

Since the differences between the differences of the y-values is not consistent, the ordered pairs do not represent a quadratic equation.

The correct option is D.

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