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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.$$y=(x-3)^{2}$$

(b) $3(\mathrm{c}) 3$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Missouri State University

Harvey Mudd College

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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all right. The best way to approach this problem is to know that this is a parabola. I was X square, and you can make a table of values and plug in zero wine and two in for X. Um, because one squared is 12 squared is four. That's why I put those points on there and the same thing with negative numbers. Well, when you square negative, it becomes positive. Negative. One times negative one is positive. One negative. Two times negative. Two is positive for, um, So then when you examine y equals X minus three squared. And you know the transformation that this shifts every point on that curve, right? Three units. Um, well, all I need to do is is pick 24 and move it to the right three. So it becomes 54 You can double check that. This is right. If I plug in five in four x five minus three is two. Once you square to you get four. So this point gets shifted right through this point. 123 this 0.123 this 0.123 And that's what your curve looks like. You can double check that this is correct with the graphing calculator. If I hit every single point, I wanted to circle that because that is one part of your answer. Um, And then you can look at that and say, Well, my X intercept for part B is going to be where Across the X axis. Well, it looks like it touches that actually goes. 123 Well, you can algebraic. We figure out that that's correct by plugging in zero for Why that's how you find X intercepts So you can solve that now by square root in each side square in the square. Cancel. Uh, the square 20 is zero. And then add three over and you can see algebraic Lee. That the X intercept really is zero plus three, which is three. So there's the rest of the answers. Yeah,

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