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Find the equation of the parabola with (a) focus at $(h, k+p)$ and directrix $y=k-p .(\mathrm{b})$ focus at $(h, k-p)$ and directrix $y=k+p$

$$\text { (a) }(x-h)^{2}=4 p(y-k) \text { (b) }(x-h)^{2}=-4 p(y-k)$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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01:26

Find an equation of the pa…

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Find the equation of the p…

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Discuss/explain how to fin…

now, knowing what we know about the equation of a problem from what we found in the previous problem, we want to know the equation of the problem with a focus at H K plus P. So the age right there tells us that we're going to be shifting um H units to the right. So we're going to have I have yeah, eight units shifted to the right and then we're going to be having a the focus shift up K Units. So it's going to be four p. Why minus K. Yeah, it's gonna look like that. And then we'll also have x minus h squared negative for p y minus K. Um in the second scenario mm.

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