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ACT Math: Coordinate Geometry Drill 3, Problem 3. What is the standard form equation for the line?
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ACT Math: Coordinate Geometry Drill 1, Problem 3. Solve the inequalities and choose the correct graph.
ACT Math 5.5 Coordinate Geometry 224 Views
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ACT Math: Coordinate Geometry Drill 5, Problem 5. What are the x-intercepts of this parabola?
Transcript
- 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.
Full Transcript
- 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.
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