Describe in words the graph of each of these curves below. Please Include in your description the shape, alon

Question

Describe in words the graph of each of these curves below. Please Include in your description the shape, along with other possible relevant information such as length, width, and center points.

a. Y = 3X2

b. (X-1)2 + (Y-8)2 = 16

c. (X+2)2 + (Y-4)2 = 36

d. Y = X2 - X

Answer 1

Hi,
a. y = 3x² ( I assume you intended the 2s as exponents in all problems.)
This is a parabola with vertex at the origin (0,0). It is somewhat narrower than a parabola with a coefficient of 1.

b) This is the equation for a circle. The standard equation for a circle is:
(x-h)² +(y-k)² = r² Where the center is at (h, k) and the radius is r.
So, this is a circle with center (1,8) and r =4. Notice that the values of h and k do not include the minus signs in the formula.

c) This is again a circle. The center is at (-2, 4) and the radius is 6. The first term is (x- (-2))² = (x+2)² . So, h = -2.

d. This is a parabola, as are all x² expressions of this type.
1) The graph crosses the y-axis at the point where x=0. So, we let x = 0 and solve for y in the equation:
y = (0)² - 0
= 0
So, the graph crosses the y-axis at the point (0,0).
2) The vertex is:
x =- b/(2a) (From the equation ax² +bx +c = 0.
So, b = -1 and a = 1
x = - (-1)/(2*1)
x = 1/2
Now, to find the y-coordinate, substitute this value in the equation for x.
y = x² -x
= (1/2)² - 1/2
= 1/4 - 1/2
= -1/4
So, the vertex is at (1/2, -1/4)

3) Finally, there is one other zero. We can find that by factoring the equation:
x² -x = 0
x(x-1) = 0 (Factor out the greatest common factor.)
Now, we set each term equal to zero and solve for x
x = 0
x-1 = 0
x = 1
So, the zeros are x=0 and we found before, and x = 1.

That should do it.
Hope this helps.
FE