Which is a zero of the function defined by 2x^2-24x+72

Answer 1

Hi, we need to set that parabola equal to 0 to find the zeros.

2x² - 24x + 72 = 0 <---- First, I notice that all terms are even. Let's divide everything by 2.

x² - 12x + 36 = 0 <---- Now, we need to factor this out. Using the AC Method, we need two numbers that multiply to 36 and add up to -12. Factors of 36: 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6. Also, all negatives work too (-1 and -36, -2 and -18, -3 and -12, -4 and -9, -6 and -6). Which of these pairs can be added to get -12? -6 and -6!

So we go from x² - 12x + 36 = 0 to the following:

x² - 6x - 6x + 36 = 0 <---- Factor this:

x (x-6) -6 (x-6) = 0

(x - 6) (x - 6) = 0 <----- We need to set this equal to zero to get the zeros. Since they are the same, we only do it once.

x - 6 = 0

x = 6

This is your x value of the zero. x = 6. You can also say (6,0) as the point on the graph.