Given f(x) = –2(x - 3)2 + 6, explain how you know:

Question

the direction of opening for the parabola.

b) the number of zeroes this parabola has.

Answer 1

f(x)=-2(x-3)^2+6

the parabola opens downward because of the minus sign (-) in front of the 2

f(x)=y

let y=0 and solve for x

0=-2(x-3)^2+6

divide both sides by -2

0=(x-3)^2-3

0=x^2-6x+9-3

x^2-6x+6=0

use the quadratic equation

(6±√12)/2

(6±2√3)/2

3±√3

3±1.732

x=4.732 and x=1.268 so the parabola has 2 zeroes

Answer 2

a) If you put this equation on a graph, you'll be able to see the direction of the opening for the parabola.

Try plugging in numbers like 0, 1, 2, 3, and 4 into x to get a number for y. You'll start to see the parabola and which way it opens.

Bonus points: change your equation to f(x) = 2(x-3)^2+6 and do this same process. Which way does the parabola open this time?

b) How many times does this parabola cross the x-axis? This is how many zeroes this parabola has.