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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.$$y=4(x-1)^{2}$$

(b) $1(\mathrm{c}) 1$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Oregon State University

McMaster 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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as long as you know the transformations for the parent function blank was square in this graph is not too difficult. Uh, it's a quadratic. So it's a parable. Uh, if you want specific points, it hits the origin. When x one or X is negative, one will square those pieces and you get positive on the same thing with explain to or negative to, you get the same positive for for either of those. So, as you look at the graph of why he was four, that's minus one squared. All you're doing is you is shifting, right? One. Uh, and I should also mention that that four is a stretch. Um So what that means is, if you were to plug in a value for, let's say, X equals one. Well, one minus one is zero squared is still 04 times zero is still zero. But when you plug in a number like zero or two, let's do two to minus one is one squared is one times four. It gets stretched. So instead of hitting the point right here, it goes all the way up to four. Same thing with zero goes all the way up to four. So it's a narrower graph than the one I drew over here. Uh huh. I'll do like a black. This one's how wider. But the graph of this one's really narrow. It's a skinny, but as far as the X intercept goes, the X intercepts where we cross the X axis, it's still going to be one, and you can algebraic. We figure out what the X intercept is by plugging in zero. For why? Because that's what it means to be The X intercept is why go zero. Well, if your first thing you do is divide the 4/0 divided by four is still zero, Then square root both sides to undo the square. Well, the square root of zero is still zero, and then your last step would be to add one over in zero. Plus one gives you an X intercept of one. No matter how you solve it, you'll get the same answer. Mhm. So here's a E N. C.

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