Simple Function (x & y intercepts)

[synthetic.]

Homework Statement

For the function f(x) = 1/4 (x=2)^2 - 4, I'm confused with regards to finding x & y intercepts.

Homework Equations

The Attempt at a Solution

You can work them out from the function in its current form, i think? For y-int, let x=0, which leaves (0,-3).

For x-nt, i done as follows;

1/4 (x+2)^2 = 4
(x+2)^2 = 16
x+2 = $$\pm$$ 4

x=2, x= -6



But then also one could use the quadratic formula, working from


1/4 (x^2 +4x +4) -4
1/4x^2 + x -3

Which gives intercepts 3/2, and -1/2


And also f(4x)= (x+2)^2 - 16
= x^2 + 4x - 12
=(x-2)(x+6)

4x=2, 4x= -6

x=1/2, x= -3/2






So, 3 different sets. What am i missing? I mean, I'm certain that the vertex lies at (-2,-4), so x=2, x=-6 must be the correct intercepts - but why are the others wrong?



Thanks.

 

[HallsofIvy]

Homework Statement

For the function f(x) = 1/4 (x-2)^2 - 4, I'm confused with regards to finding x & y intercepts.

Homework Equations

The Attempt at a Solution

You can work them out from the function in its current form, i think? For y-int, let x=0, which leaves (0,-3).

For x-nt, i done as follows;

1/4 (x+2)^2 = 4
(x+2)^2 = 16
x+2 = $$\pm$$ 4

x=2, x= -6



But then also one could use the quadratic formula, working from


1/4 (x^2 +4x +4) -4
1/4x^2 + x -3

Which gives intercepts 3/2, and -1/2

No, it doesn't. here "a" is 1/4, "b" is 1, and "c"=-3 so
x= (-1+ sqrt(1-(4(1/4)(-3)/(2*1/4)= (-1+ sqrt(4))/(1/2)= 1/(1/2)= 2 and
x= (-1- sqrt(1-(4(1/4)(-3)/(2*1/4)= (-1- sqrt(4))/(1/2)= -3/(1/2)= -6.

Did you forget the "a" in the "2a" in the denominator?

And also f(4x)= (x+2)^2 - 16

No, f(4x)= (1/4)(4x- 2)^2-4. Did you mean 4f(x)? If f(x)= 0, then 4f(x)= 0 for exactly the same x.

= x^2 + 4x - 12
=(x-2)(x+6)

which gives the roots you got initially.

4x=2, 4x= -6

x=1/2, x= -3/2

But it was NOT 4x, it was 4f(x)

So, 3 different sets. What am i missing? I mean, I'm certain that the vertex lies at (-2,-4), so x=2, x=-6 must be the correct intercepts - but why are the others wrong?



Thanks.

You weren't "missing" anything- just did the algebra wrong.

 

[synthetic.]

Did you forget the "a" in the "2a" in the denominator?

Ohhh. Damn. Yes, sorry, and thanks. I often do that actually, */2 instead of */2a using the quadratic formula. I must stop.

Thanks, Hallsofivy.