What is a common factor of both x^2-9 and x^2+x-6
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Answer:
Step-by-step explanation:
If you plot the focus and the vertex, you see that the focus is on the same vertical line, just 4 units up. Since the vertex is below the focus and a parabola ALWAYS wraps around the focus, the parabola is a positive y equals x-squared type. Depending upon what you call standard form will dictate how your answer "looks", although they are both the same parabola. There are 2 forms:
and
We will work on the first one, then rewrite it into the second one.
Our h value is -5, our k value is 2 (from the vertex (h,k)), and p is defined as the distance between the focus and the vertex. Our p is 4. Filling all that in:
That's one form. If we expand the left side of that form we have
Now divide both sides by 16 to get
Now add 2 to both sides in the form 32/16 to get
They are both the same parabola; pick whichever one fits your needs.