ShmoopTube

00:02

Here's your shmoop du jour, brought to you by the Parabola Virus. Much less dangerous

00:07

than the Ebola Virus, especially since... it doesn't exist.

00:12

What are the x-intercepts of this parabola:  y -- 3 = 2x squared + 2x?

00:18

And here are your potential answers...

00:23

It's really asking whether we understand what x... intercepts.

00:27

So just to refresh, an x-intercept is when the graph intercepts the y-axis.

00:32

So... wherever y equals 0.

00:39

To find the x-intercepts, set y equal

00:42

to 0 in the equation. 0 minus 3 equals 2x squared plus 2x. 0 minus

00:49

3 is negative 3...and then we can add 3 to both sides.

00:53

0 equals 2x squared plus 2x plus 3. Looks like a quadratic equation we can solve with

00:59

the quadratic formula.

01:01

x equals negative b plus or minus radical...b squared minus 4ac all over 2a...

01:07

...with a equal to 2, b equal to 2, and c equal to 3. Let's plug these into our equation.

01:14

x equals negative 2 plus or minus radical 2 squared minus 4 times 2 times 3...which

01:20

equals 4 minus 24 equal to -20 under the radical... all over 2 times 2... or 4.

01:27

But note that there's a NEGATIVE number under the radical...which tells us that both of

01:31

the solutions to this equation are... imaginary.

01:37

It means that the parabola doesn't

01:39

cross the x-axis. So no x intercepts exist. Answer choice E.

Full Transcript