Which value of K will make x^2-1/4x+k a perfect square trinomial?

Mathematics

1 answer:

lakkis [162]3 years ago

4 0

To find it it is
ax^2+bx+c
if the first term (a) is 1 then c=b/2
b=-1/4
(-1/4)/2=-1/4 times 1/2=-1/8

k=-1/8

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gizmo_the_mogwai [7]

Answer:

Yes the relationship is linear and given by:

$y+2=-\frac{5}{4} \,(x+9)$ (first option of your list)

Step-by-step explanation:

Yes, it is a linear expression. As we did in previous exercises, we calculate the difference between consecutive y values of the table, and write down the answers we get:

-7-(-2) = -7+2 = -5

-12-(-7) = -12 +7 = -5

-17 - (-12) = -17 + 12 = -5

We notice that all of them give "-5"

Now we evaluate the difference between consecutive x-values in a similar fashion:

-5 -(-9) = -5+9 = 4

-1-(-5) = -1+5 = 4

3-(-1) = 3+1 = 4

We see that they all give 4 as the difference.

That means that the rate of change $\frac{y_2-y_1}{x_2-x_1} =\frac{y_3-y_2}{x_3-x_2}=\frac{y_4-y_3}{x_4-x_3}=\frac{-5}{4}$

This means that the slope (rate of change) of the line is "-5/4"

We can now use the general point-slope form to write the equation of the line, using the first pair of the table as our selected point, and using "-5/4" for the slope:

$y-y_0=m\,(x-x_0)\\y-(-2)=-\frac{5}{4} \,(x-(-9))\\y+2=-\frac{5}{4} \,(x+9)$