Find the x intercepts of the parabola with vertex (5,-12) and y intercept (0,63)

The equation for the standard form of parabola is given as:

y = A (x - h)^2 + k

with (h, k) being the (x, y) coordinates of the vertex

For the given problem, we are given that (h, k) = (5, - 12).
We can then use point (0, 63) for x and y to solve for A
63 = A (0 - 5)^2 - 12
75 = A (25)

A =  75 / 25

A = 3

Equation of given parabola: 
y = 3 (x - 5)^2 - 12

We can now solve for the x –intercept:
Set y = 0, then solve for x

0 = 3 (x - 5)^2 - 12

3 (x - 5)^2 = 12

(x - 5)^2 = 4

Taking sqrt of both sides
x - 5= ±2

x = -2 - 5 = -7 and x = 2 - 5 = - 3
x = -3, -7

x-intercepts of given parabola: -3 and -7

(-3, 0) and (-7, 0)

832 inches squared.

Step-by-step explanation:

Composite shapes' surface areas can be found by taking the individual geometrical shapes' surface areas. After doing so, add together the surface area, but make sure to subtract any overlapping area.

For this instance, you have a cube placed on top of a rectangular prism.

A cube's surface area is defined as ., in which is defined as the side length of the cube.

A rectangular prism's surface area is defined as , in which the side lengths of the width, length, and height are used as W, L, and H.

The cube's surface area when the side length is 9 inches is 6 * (9)^2, or 486 inches squared.

The rectangular prism's surface area when side lengths are 14, 11, and 4 inches is A = 2(11*14 + 4*14 + 11*4), or 508 inches squared.

To calculate the composite area, the areas of the overlapping sections must be subtracted. Because there is a 9x9 area on the cube and a 9x9 area on the prism overlapping, you must subtract 2* (9)^2, or 162 inches squared, from the total area of 994 inches.

994 - 162 = 832 inches squared.