SAT Free-Response problem...?

johny

Hello. Could someone help me figure out how to get to the answer in this problem?

Let the function h be defined by h(x)=14+(x^2/4). If h(2m)=9m, what is one possible value of m?

The answer can be both 2 or 7, but HOW do I get there?!

anonymous

Hi Johny,

We know h(x) = 14 + (x^2)/4. We need to find h(2m). So plug this into the function. Everywhere there is an x in the function, plug in 2m.

h(x) = 14 + (x^2)/4

h(2m) = 14 + ((2m)^2)/4

h(2m) = 14 + ((2^2)(m^2)) /4

h(2m) = 14 + (4m^2)/4 The 4s cancel out.

h(2m) = 14 + m^2.

The question tells us that h(2m) also equals 9m, so set these two values equal:

h(2m) = 14 + m^2

h(2m) = 9m

So 9m = 14 + m^2

Now it's up to FOIL:

9m = 14 + m^2

m^2 - 9m + 14 = 0

(m - )(m - ) = 0

(m - 2)(m - 7) = 0

m =2 and m = 7

I hope that helps!

anonymous

Derive derive derive drive

anonymous

you should ask your teacher @_@