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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.$$y=3(x+1)^{2}-3$$

$$\text { (b) }-2,0(\mathrm{c})-2,0$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Oregon 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, So what we're doing is we're examining this graph three X plus one squared, minus three. Um, so as long as you know the parent function of y equals X squared and you know the transformations. So y equals X squared is the parabola that's Vertex is at the origin opens up. Um, yeah, I don't want to get into what that is, because what we really care about is that this transformation is shifting. Right? One, this is shifting down three because the minus. So that's where your new Vertex is at is one negative three. I said the wrong day night. All right, Mhm. Okay. Remember, it's backwards. You want to go left? One. So it should have been negative one. There we go. Uh, so on your graph. And if you don't believe me that this is the right point, uh, for your vertex, you can always plug in X equals negative one. Well, if you plug in negative one for X +10 square, +20 times. Anything is still zero minus three is negative. Three. So what this three does that's in front is a stretch to vertical stretch. So normally that the parabola opens up like up 1/1. Well, instead, what it does is goes up 3/1 and also backwards up 3/1. Now you have to be careful with this because it is a U shape. So the next one is not going to be up 3/1. It's going to be even narrower. Uh, as you go up to get that u shape. But this is what your graph looks like. That's your answer to part A and part B. It appears like your X intercepts our values of negative two and positive zero. So I'm gonna circle that. That's what you get to guess. You can confirm that That's right, by plugging in zero for why. And that's how you find X intercepts, Algebraic Lee and the process to do this. Then, as you add three over, cancel that out. Zero plus three is three, then divide by three. Well, three Divide by three equals. Ones are looking at that quantity of X plus. One squared is equal to one. Well, now, when you square root, make sure you that you square root both the positive one and a negative one, because what's inside of that. Parentheses could have been a negative, because when you square negative to positive, so then what you need to do next to subtract that one over and you can get one X intercept to be negative, too. And when you subtract one over on this one, you get the other X intercept to be zero, and that's your work for letters C to confirm that your answer was correct. From Letter B. There's a, B and C.

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