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(a) Draw the graph of the parabola. (b) From your graph, estimate the $x$ -intercepts. (c) Check your estimate by finding the $x$ -intercepts exactly.$$y=(x-2)^{2}$$

(b) $2(\mathrm{c}) 2$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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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(a) Draw the graph of the …

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if you look at the parent function of Y equals X squared. That's a parabola that is at the origin because and you can make a table of values if you want. If you plug in zero square 20 you plug in one or negative one. Whether you square one or negative one, you always get positive. One. They're the same thing with two. Negative to step up. Two squared is four negative. Two squared as possible because negative two times negative two is a positive number. Uh, so this is what the graph looks like of that quadratic. That's that's called. So when we examine, why equals X minus two squared, the transformation is shifted. Right. Cheap. So, um, I'm gonna take all of the points that we have on here, and I'm just gonna move them to the right to units. So this point gets shifted to the right to units. This point gets shifted to the right to units. Then native to four shifted right two units and then to four gets shifted right, two units. So we're at 44 Um, if you're confused by the transformation, start plugging in values for X like plug in to infer x two minutes to zero squared zero. Um, you know, plugging three francs, three minus two is 11 squared is one. So that's why all these points are like that. So I'm going to circle that blue curve, Um, and then in part B, they're just asking you to estimate the X intercept. Well, looks like across the X axis at two, but you can algebraic. We figure that out by plugging, uh, putting zero in for y. That's how you algebraic. We figure out the Y intercept. So when you square root both sides that cancels out the square. Uh, this where 20 is zero and then add to over old zero plus two is the correct It's intercept of two. So as part seat, yeah.

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