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4 years ago

F(x) = 5x2 − 70x + 258. Complete the square.

Mathematics

1 answer:

astraxan [27]4 years ago

7 0

5(x^2 - 14x + 258/5)
= 5((x-7)^2 -49+258/5)
= 5((x-7)^2 + 13/5)
= 5(x-7)^2 + 13
I belive this is how it should be done

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3 years ago

Write the standard form of the equation of the circle with endpoints of a diameter at the points (7,2) and (-9,5).

lys-0071 [83]

Answer:

$(x+1)^2 + (y- 3.5)^2 =64$

Step-by-step explanation:

We are given that endpoints of a diameter at the points (7,2) and (-9,5).

Center of the circle is the mid point of diameter

So, first find the mid point of diameter

Formula : $x=\frac{x_1+x_2}{2} , y=\frac{y_1+y_2}{2}$

$(x_1,y_1)=(7,2)\\(y_1,y_2)=(-9,5)$

Substitute the values in formula

$x=\frac{7-9}{2} , y=\frac{2+5}{2}$

$x=-1 , y=3.5$

So, center of circle = (h,k )=(-1,3.5)

To find length of diameter :

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(x_1,y_1)=(7,2)\\(y_1,y_2)=(-9,5)$

$d=\sqrt{(-9-7)^2+(5-2)^2}$

$d=\sqrt{265}$

Length of radius = r = $\frac{Diameter}{2}=\frac{\sqrt{256}}{2}$

Standard form of the equation of the circle : $(x -h)^2 + (y- k)^2 = r^2$

(h,k )=(-1,3.5)

$r=\frac{\sqrt{256}}{2}$

Equation of the circle : $(x+1)^2 + (y- 3.5)^2 =(\frac{\sqrt{256}}{2})^2$

Equation of the circle : $(x+1)^2 + (y- 3.5)^2 =64$

Hence the standard form of the equation of the circle with endpoints of a diameter at the points (7,2) and (-9,5) is $(x+1)^2 + (y- 3.5)^2 =64$

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4 years ago

Which statements describe one of the transformations performed on f(x) = x^2

SashulF [63]

Answer:

The correct options are C and D

C. A translation of 5 units up

D. A reflection about the x-axis

Step-by-step explanation:

We have been given as function of the graph:

f(x) = x²

Which is transformed into the function

g(x) = -(x-2)² + 5

Consider the graph of y = x²

To convert it into the graph of given transformed function.

First reflect the graph over x-axis, the equation becomes

y = -(x)²

Then translate the graph 2 units to the right

y = -(x - 2)²

Then translate the graph 5 units up.

y = -(x - 2)² + 5

Thus, the correct statements are C and D

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3 years ago