Question

can you please solve these questions.
Use completing the square to show that the vertex for f(x) = x2 + x – 2 is at (-1/2, -2 ¼). Use
fractions, not decimals, in your work.
2) Show that the vertex for g(x) = 3x2 + 18x + 15 is (-3, -12) by averaging the x-intercepts. This will be
easier if you factor out the 3 first.
3) Find an exponential equation that passes through (2, 50) and (4, 1250).
(Answer: 2•5x
Show all the algebra necessary to get this answer.)

Answer 1

#1. x^2+x-2 = x^2+x + 1/4 - 2 - 1/4
= (x + 1/2) - 9/4

#2. for ax^2+bx+c, the vertex is at x = -b/2a
So that is at x = -18/6 = -3
g(-3) = -12

#3. y = a*b^x
ab^2 = 50
ab^4 = 1250
divide, and b^2 = 25
so, b = 5 (why not also -5?)
a = 2
y = 2*5^x