Complete the square to find the vertex of this parabola. x2 + 10x - y + 15 = 0​

y

=

x

2

−

10

x

+

15

Rewrite the equation in vertex form.

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y

=

(

x

−

5

)

2

−

10

Use the vertex form,

y

=

a

(

x

−

h

)

2

+

k

, to determine the values of

a

,

h

, and

k

.

a

=

1

h

=

5

k

=

−

10

Find the vertex

(

h

,

k

)

.

(

5

,

−

10

)

image of graph

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

his first public project he is asked to create a small scale drawing. the garden is a right triangle with base 25m and height 30m. are you trying to solve for the last side/hypotenuse? the irrational form of the answer would be 5\sqrt{61}