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

(b) -1 (c) -1

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

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Lectures

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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 my expectation is that students know the parent function of Y equals X squared. A quadratic is a shape of a prevalence a U shaped curve because as you get larger values for X, like when X is 11 squared is one when X is 22 squared is four. Um, and it keeps growing very quickly. Uh, negative values are also positive because when you square a negative, uh uh, negative one times they want is positive. So what happens when we look at the craft of negative three and then X plus one squared? Well, the big thing that we care about is that this graph has shifted. Left one, um and then this three makes it a stretch of three. But the other vertical stretch of three I should say the other pieces that negative. This is an X axis reflection. So as you go through all of the transformations and you can plug in certain values for X like plugging in negative one for X because negative one plus 10 square to still zero times anything is still zero. But if you were to plug in zero for X well zero plus one is one squared is one times negative. Three. Get that negative answer. So now it's a downwards. Uh huh. Downwards. Per abalone. Um, and you can do the same thing with plugging in negative two in forex and see that the graph is going down at that point. So this is what the graph looks like. This is part a. So then part B, you can estimate that the X intercept will be negative one. Well, you can verify that. That's true. By setting that equation equal to zero, because the X intercept is one y equals zero. So my first step would be to divide that negative three over because zero divided by anything is still zero. Uh, and then square root both sides Cancel that out. All the square root zero is still zero, and then subtract 1/0 minus one is negative one. So when you algebraic, we figure out the x intercept, You just confirm your graphic, uh, graph that you did it correctly. Your X intercept is right. So here's a B. C.

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