What is the equation in the standard form of a parabola with a vertex of (4,2) that passes through (2, 14)?

9514 1404 393

  y = 3x^2 -24x +50

Step-by-step explanation:

The vertex form is ...

  y = a(x -4)^2 +2

where 'a' is chosen to make the curve pass through the given point.

  14 = a(2 -4)^2 +2 . . . . substitute the given point

  14 = 4a +2 . . . simplify

  12 = 4a . . . . . subtract 2

  3 = a . . . . . . . divide by 4

Then the standard form is the expansion of the vertex form:

  y = 3(x -4)^2 +2 = 3(x^2 -8x +16) +2

  y = 3x^2 -24x +50

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