Which set of numbers includes only integers?
2 answers:
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Answer:
x = -1 <--- axis of symmetry
(-1, -9) <-- vertex
2, -4 (or, in my old precalc class we wrote our roots as (2,0) and (-4,0)) <--- roots
Step-by-step explanation:
a) Axis of symmetry equation is defined as
= x (i memorized this)
Quadratic equation form:
And our original equation:
So..
So our axis of symmetry is at x = -1,
b) now vertex point can be found by plugging this value back into our original equation.
y =
y = 1 - 2 - 8
y = - 9
So our vertex is at (-1, -9)
c) Finally, lets factor
= 0 (when finding the roots, set y = 0, because we are trying to find where we cross the x-axis)
= 0
x = 2; x = -4 <--- Roots
The equation of parabola is
Comparing with the vertex form of the parabola:
Hence, the vertex of the parabola is given by (h,k) = (1, -2)
Now, vertex is the midpoint of the focus and the point on the directrix.
Distance, between vertex and focus is p and that of point on the directrix is p.
Now, let us find p
Thus, the focus is given by
And the directrix is given by
Since, a >0 hence, it is an upward parabola.
The graph is shown in the attached file.
