Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

In Exercises 17-34, sketch the graph of the quadratic function without using a graphing utility. Identify the vertex, axis of symmetry, and x-intercept(s).

$ f(x) = - x^2 + 2x + 5 $

$f(x)=-1(x-1)^{2}+6$$(h, k)=(1,6)$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Parker P.

October 18, 2021

what are the x intercepts

Harvey Mudd College

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

05:01

In Exercises 17-34, sketch…

03:43

04:41

04:50

04:12

05:25

03:42

03:26

04:55

03:48

03:59

03:21

05:39

05:24

02:46

08:40

Using Standard Form to Gra…

12:02

03:44

In Exercises 35-42, use a …

03:31

for this problem. Let's write this in the Vertex form. Okay? Which is X minus age Swear plus que or the Vertex is the point h k and we'LL see why the point of doing this in a few moments are simplified the problem So first let me fat throughout this negative from the ex term So I'll just leave the plus five outside now complete the square inside the parentheses So you take half of negative too That's negative one and then you square that quantity you get one So add that won it and notice We didn't really add one because of this negative sign out here we really subtracted one Some will make up for this by adding one outside here Now we've completed the square so we have X minus one squared plus six and so graphing F is the same as graphing this quantity this polynomial over here and notice that if you start with x squared we can do transformations to build up our function f so we'Ll just graph each of these transformations And when we reach the final one we'LL have the graph of f So first we have x square so we know what this graph looks like. Something that Daddy Ex Claire. The next one we subtract one from the ex. So this is a shift One unit to the right. So each point on this X squared graft is shifted over one unit to the right. So this is the second Graff X minus one square. Next up, we have a negative outside. So this is a reflection about the X axis. So each point on the red graft each of these y values gets multiplied by a negative one. So here we have four. So now I have negative forward out here. There's a one. So now we go to negative one zero stays negative one and then negative for So this is the graph. And then finally, the last step here is to add six on outside, not to the experts of the whole function. So this is a shift. Six units upward. So each point each y value and green goes up by six. So here we have. Why is negative for So we add six to that putting us at two. Here. We had negative one. So add six to that putting you in five here we have zero That puts us at six and then back to five and then back to two. And there we are in blue. This will be our final answer, or at least for the graph. Okay, so that completes the first part. And then now we identify the Vertex. Well, the Vertex. We can either see that from the graph. Or you could also see it from the Vertex form that we found earlier. Access of cemetery. This is always the equation X equals h urge the X coordinate of the Vertex sonar case one that would be our access of symmetry. And we could even have a rough sketch of that. This is very cool. Fine. Passing right through the verse six. And next we have the ex intercepts. So well, go ahead and set f of X equals zero and then solve this for X and then go ahead and saw that for X. And you should get one plus or minus route six. So if you do the minus sign. That's this rule over here this x intercept and then if we do this one over here, this is the plus time before the square root of six

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, the absolute value or modulus |x| of a real number x is its …

In Exercises 17-34, sketch the graph of the quadratic function without using…

Using Standard Form to Graph a Parabola InExercises $17-34$ , write the …

In Exercises 35-42, use a graphing utility to graph the quadratic function. …

06:17

Use power series to solve the differential equation.

$ (x - 3)y'…

04:14

In Exercises 13-16, graph each function. Compare the graph of each function …

01:55

Show that a conic with focus at the origin, eccentricity $ e $, and directri…

02:13

Solve the differential equation.

$ y'' + 2y = 0 $

01:18

In Exercises 89 - 92, use a graphing utility to graph the function.…

01:56

$ 2 \dfrac{d^2y}{dt^2} + 2 \dfrac{d…

01:21

Write a polar equation of a conic with the focus at the origin and the given…

A rancher has 200 feet of fencing to enclose two adjacent rectangular corral…