finding y intercepts of y = (1/2)(x - 2)^2 + 3

[btrfly24]

I'm having a huge brain fart. I'm working with parabolas and finding x and y intercepts, by using the focus, vertex, and directrix. I get everything except I can't seem to do the math right to solve for the intercepts. Here's the problem:

y = (1/2)(x - 2)^2 + 3

I've got everything else I just can't figure out how to solve to get the x intercepts.

 

[luthien]

To find x-intercepts, you need to find where the curve crosses the x-axis. That means you want to know for what values of x the value of the function is 0.

So...set y=0 and use quadratic formula.

 

[jwpaine]

there are no solutions for that equation. (the parabola doesn't hit the x-axis)

expand 1/2(x-2)^2 +3 gives you 1/2x^2-2x+5

the discriminant will tell you how many real solutions you have... you can also check by graphing to see that there are no x-intercepts

discriminant = b^2-4ac = ((-2)^2 - 4(1/2)(5)) = -6

The discriminate is less than 0, thus your equation has 2 imaginary solutions which you can find by completing the square, and solving for x (you will end up with 1 +/- the squareroot of a negative number)

EDIT: you said y-intercept, sorry.