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

(b) $1(c) 1$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

McMaster University

Harvey Mudd College

Baylor University

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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(a) Draw the graph of the …

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So if we know the graph of likewise X squared the quadratic parent function and some people even make a table values like when you plug in negative one squared, you get positive. One plug in negative two squared is positive for, um, you get this u shaped curve. That's why we call it a parabola, Um, for a quadratic. And that should help you. If you know the transformations of now you have two x minus one squared. You can look at that and say, Okay, it's shifted to the right one. The negative in front is a reflection over the y axis. I said that wrong over the X axis. Um, this two makes it a stretch, but we really don't care about that right now, because when you look at the graph of that and we go through the transformation right one, and you can confirm that that's the right point, because if you plug in one for X one, minus one is zero squared is still zero times. Anything is still zero. Uh, and where it gets more interesting is when you plug in zero or you plug in to in forex, you'll get the same answer because to minus one is one square. It is one times negative two, because you're negative to you would have gotten the same answer here, Um, so you can actually see the stretch a vertical stretch by a factor of two. Um, and the reason why it's going down is because of that negative. So there's your answer to part A and part B. They just ask you Well, what is the X intercept? It appears like from the graph that the X intercept does that want. So you can confirm that that's right, because the X intercept is when y equals zero so you can set that equation equals zero and you can go through and you can solve for X. Now they can divide negative two over. Well, zero divided by anything is still zero. Take the square root, you can solve the square. Well, zero square root is still zero, and then add one over. Well, zero plus one is one. So you can confirm that your X intercept is one for part c. And there's your third answer. The graph is a and then the two X intercepts, and they match. So we did it, right? Yeah,

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