1)What is the distance between the museum and sailing club.I cant post the graph or anything but I have my numbers right its 53 but I used the distance formula so its either 53 units or the square root of 53 units.

2)Write the equation of the parabola y= 4x^2-8x+1 in standard form
answer= y= 4(x-1)^2-3

3)Write an equation for the parabola with focus (1,3)and vertex(0,3)
answer= x= 1/4(y-3)^2

4)Write an equation for a circle if the endpoints of a diameter are at (1,1)and(1,-9)
answer= (x-1)^2+(y+4)^2=25

5)Which is the equation of a circle with center (0,1)and radius 2 units?
answer= x^2+y^2-2y=4

1) To find the distance between the museum and sailing club, you need to use the distance formula. Make sure you have the coordinates of both locations. The distance formula is given by:

Distance = sqrt((x2-x1)^2 + (y2-y1)^2)

Plugging in the coordinates, the distance between the museum and sailing club would be either 53 units or the square root of 53 units, depending on whether you use the actual numbers or keep the square root symbol.

2) To write the equation of the parabola y = 4x^2 - 8x + 1 in standard form, you need to complete the square. The standard form of a parabola equation is y = a(x-h)^2 + k.

First, factor out the common coefficient of 4 from the quadratic terms:
y = 4(x^2 - 2x) + 1

Then, complete the square by taking half of the coefficient of x (-2) and squaring it, which gives (-2/2)^2 = 1:
y = 4(x^2 - 2x + 1) + 1 - 4

Simplify further:
y = 4(x - 1)^2 - 3

So, the equation of the parabola in standard form is y = 4(x - 1)^2 - 3.

3) To write an equation for a parabola with focus (1,3) and vertex (0,3), you need to use the standard form of a parabola equation: x = a(y - k)^2 + h.

Since the vertex is (0,3), the equation becomes x = a(y - 3)^2 + 0.

The focus is (1,3), which means the distance between the vertex and the focus is the same as the distance between the vertex and the directrix. The directrix is a horizontal line.

Using the distance formula, the distance between (0,3) and (1,3) is 1 unit.

So, the equation for the parabola is x = 1/4(y - 3)^2.

4) To write an equation for a circle if the endpoints of a diameter are at (1,1) and (1,-9), you need to find the center and the radius.

The center is the midpoint of the diameter, which is located at (1, (1+(-9))/2) = (1,-4).

The radius is half the length of the diameter, which is the distance between the endpoints.

Using the distance formula, the distance between (1,1) and (1,-9) is 10 units. So, the radius is 10/2 = 5 units.

The equation for a circle is given by (x-h)^2 + (y-k)^2 = r^2, where (h, k) is the center and r is the radius.

Plugging in the values, the equation for the circle is: (x-1)^2 + (y+4)^2 = 25.

5) The equation of a circle with center (0,1) and radius 2 units can be found using the formula (x-h)^2 + (y-k)^2 = r^2.

Plugging in the given values, the equation becomes: (x-0)^2 + (y-1)^2 = 2^2.

Simplifying further: x^2 + (y-1)^2 = 4.

So, the equation of the circle is x^2 + (y-1)^2 = 4.