Graph the quadratic equation y = 3x2 + x – 3.
Let's find the useful things. Other than duct tape, a Swiss army knife and a compass. We meant more within the realm of algebra. We should have been clearer.
1. What are the intercepts?
To find the x-intercepts, we need to use the quadratic equation because this polynomial doesn't factor nicely. We find
For the purposes of graphing, we can round these numbers to 0.8 and -1.2:
The y-intercept is the constant term of the quadratic equation, or -3:
2. What is the vertex?
The vertex is at , which in this case is .
When we plug back into the equation, we find
The vertex is .
For the sake of graphing, as well as for the sake of our own sanity, we can round to (-0.2, -3.1).
3. Does the parabola open upwards or downwards?
Since the coefficient on the x2 term is positive, the parabola opens upwards. Like a blossoming flower. That's so nice.
Putting everything together, we get our graph: