# ACT Math 5.5 Coordinate Geometry

ACT Math: Coordinate Geometry Drill 5, Problem 5. What are the x-intercepts of this parabola?

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### Transcript

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

So... wherever y equals 0.

To find the x-intercepts, set y equal

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

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

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

the quadratic formula.

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

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

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

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

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

the solutions to this equation are... imaginary.

It means that the parabola doesn't

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