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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|Coordinate Geometry||Conic sections|
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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.