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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.$$y=-2(x+4)^{2}+7$$

$$-5.9,-2.1(c) \frac{-8 \pm \sqrt{14}}{2}$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Missouri State University

Campbell University

Baylor University

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 we look at this problem, Why equals negative two uh, X plus four squared plus seven. If you follow your transformations, this has shifted. Left four up seven. And that's actually where your Vertex is located. Vertex is at negative 47 and then here. This is telling me that we have a downwards parabola because it's negative. It's an X axis reflection, and they stretch of two, some people say, by a factor of two. So looking at is this graph is left for 1234567 And what I like to think about is that, like the first, uh, curve is down by two. But then the next one, because it's a steeper slope, goes down a little bit faster than that. So I'm guessing that it's going to intersect a little bit to the left of negative two. And the other thing that's important to know is that the axis of cemetery is going through the Vertex. So if I'm a little bit less than one on one side, I need to be sorry a little bit less than two. On the one side, I need to be a little bit less than two on the other. So this is what your graph would look like if you use a graphic couch later. Might get a slightly better answer. It looks like the X intercept should be about negative 5.9 and negative 2.1. Um, so then, from here, you can actually figure out the exact X intercepts because the X intercepts are when y equals zero. Um, so you can set this equation equal to zero, which is pretty straightforward, because then what you can do is you can subtract the 7/0 minus seven is negative. Seven. Cancel that divide by negative two. And so what you have is that X Plus four squared is April to seven halves. So now you can solve that by square, rooting both sides. And the only issue is we don't We don't believe the radical in the denominator, so you might rationalize the denominator. So you're looking at X Plus four equals plus or minus. Route 14 all over. Route to chapter two is four or two. Yeah, And then from there you just need to move to four over. But we typically put the same denominator, so change that to be eight has it has is equal to four. So then you can see that the exact X intercepts is negative. Eight. That way we can combine the numerator together all over to and those are your exact answers for letters C.

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