A vertical parabola goes through (1, -2), (-3, 10), and (4, 31). Use matrices to solve for D, E, and F, given the general form (since it is a vertical parabola there is not a term)

The general equation of the vertical parabola is

, where a,b and c are constant.

The parabola passes through the points D(1,-2), E(-3,10), and F(4,31).

For point D:

For point E:

For point F:

All the three equations can be written in the matrix for as:

The value of all the three coefficients can be determined by solving the above equation as

On solving this, we have

So, values of the constants,

a=2, b=1, and c=-5

Hence, the required equation of parabola is

594 square inches

step-by-step explanation:

vote !

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752