Description
Explain what each of the following represents, and how equations (a) and (b) are equivalent.
(a) y = a(x - h)2 + k, a ≠ 0
(b) (x - h)2 = 4p(y - k), p ≠ 0
(c) (y - k)2 = 4p(x - h), p ≠ 0
Explanation & Answer
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Explain what each of the following represents, and how equations (a) and (b) are equivalent.
(a) y = a(x - h)2 + k, a ≠ 0
(b) (x - h)2 = 4p(y - k), p ≠ 0
(c) (y - k)2 = 4p(x - h), p ≠ 0
(a) This equation represents a parabola that opens upward or downward. If a >0, then the
parabola opens upward and if a < 0, it opens downward. The vertex of this parabola is at
𝑎
𝑎
(h,k), and focus is at (ℎ, 𝑘 + ). The directrix is 𝑦 = 𝑘 − , and axis of symmetry is x = h.
4
4
The parabola crosses the y – axis(y – intercept) at (0, 𝑎ℎ2 + 𝑘) and the x – ...
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