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

(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.$$y=x^{2}+4 x-6$$

$$\text { (b) }-5.2,1.2(\mathrm{c})-2 \pm \sqrt{10}$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Missouri State University

Campbell University

Oregon 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).

03:18

03:11

(a) Draw the graph of the …

02:13

02:40

02:38

02:02

02:24

02:04

02:23

02:16

02:19

03:04

02:08

01:59

03:40

02:35

02:44

03:19

02:55

So we're looking at the graph of why equals X squared plus four x uh minus six. And the first thing that I might point out is that the Y intercept in this problem is the C value. So that's going to be down six. Uh, and then you can find the Vertex by using the formula X equals negative B over two A. Uh so the B value is four. So that would be negative for over two times. The A value is one. It's in front of the X squared. So negative four divided by two is negative. Two. So that tells me my accesses cemetery is to the left to and to find the Vertex. Then that's the X coordinate of the Vertex. So I have to plug in negative too here and here. So negative to when I square. It is positive for, um, four times negative two is negative. Eight minus six. We're looking at negative 10. When you simplify that, that's the Y value. So, uh, 6789 10. That's where your vertex is located. Right there. The other thing is, I mentioned the access of cemetery, so that's got to be reflected on the other side. Two units away from the axis of cemetery. You can graph that line then that curve. I should say it's not really a line now. The downside to this kind of graph is it's very difficult to see, so you might want to use a graphing calculator. And if you do that, what you'll see is this. X value is about negative 52 and this X value is about 1.2. And those numbers should make sense because it has to be the same distance away from the Axis Cemetery. Um, it looks like it's 123.2 units. Way 3.2 usually, anyway. So this is a graph that you need to do for part a. Part B is just saying that the X intercepts are what I just mentioned, and then to figure out what the actual X intercepts are, you set the situation in the zero and the music quadratic formula. The quadratic formula says to do X equals negative B plus or minus the square root of B squared minus four a. C. See, the C value is negative. Six all over to a and as you go inside of this, you'll see that we're looking at negative four plus or minus the square root. Maybe 16 plus 24. Uh mm. Which is 40 all over to now. 40. You degree. Right. As to route 10. And then when you divide each piece by two. Negative four divided by two is negative. Two and then to divide by two is one through 10. These are the actual X intercepts for part C There. See the okay and a Yeah.

View More Answers From This Book

Find Another Textbook

Numerade Educator

03:57

Compute the difference quotient $\frac{f(x+h)-f(x)}{h}, \quad h \neq 0$ When…

02:26

(a) determine the domain, (b) sketch the graph and (c) determine the range o…

03:00

Given the function defined by the equation $g(x)=2 x \sqrt{x+1}$ determine (…

01:01

Determine if the function defined by the given equation is odd, even or neit…

Solve each of the quadratics by first completing the square. When the roots …

05:27

The numerator of a fraction is three less than the denominator. Tripling the…

04:30

Let $y=g(x)$ describe the upper half of the circle $x^{2}+y^{2}+8 x-6 y+$ $…

03:22

Determine whether the given equations is a circle, a point, or a contradicti…

05:39

In each of the following exercises, solve the given inequality.$$\frac{(…

Find the slope, $x$ -intercept and $y$ -intercept of the given line.$$2 …