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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.$$y=(x+1)^{2}$$

(b) $-1(c)-1$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

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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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Okay, So the key to graphing this problem is knowing the transformations. Um, and what I'm talking about is the transformation for the y equals X squared graph that most students if your calculations, you know that when you plug in zero for X zero square to zero when you plug on one for X one square, it is one when you plug a negative one interacts negative. One squared is positive one. Um and then I'll just give you a few more points to four. Negative. 24 So if you understand the transformations you look at the graph that they give you, um, that this graph is shifted. Left one. Now, if that's confusing, think about if you were to plug in negative one. And for X uh, well, negative one plus one of the zero. Once you square zero, you get zero. That's why it shifted. Left one. It's the opposite. So if I plug in zero for X zero plus one is 11 square. It is one, um And so if you I guess pick out the rest of those points and just ship them All left. One left, one left, One left, One left one left one. Um I mean, we over here, though. Two negative three. You can see what the graph looks like. And then when they ask you to answer the question, where are the X intercepts? So let me circle this graph. That's the correct graph. Um, the X intercept is pretty clear. Is that negative one? Um, and then you can confirm that by, uh, the X intercept is when y equals zero. So if you set that equation equal to zero and you go through the solving process and you square root because the square root cancels out the square, the square 20 is zero and subtract the 1/0 minus one is negative one. So you can confirm that the X intercept is negative one. When you do that ultra graphically. So there's your final two answers.

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