Pre-Calculus-Circles and Parabolas

User Generated

xngtvey

Mathematics

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

User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Attached word and pdf. Let me know if you have any questions or need any modificaions.

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 – ...


Anonymous
I was struggling with this subject, and this helped me a ton!

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags