Use a graphing calculator to solve each equation. If an answer is not exact, round to the neares

step 1 All right, so we are looking now to be able to solve functions. So again, for this one, we're us

Use a graphing calculator to solve each equation. If an...

Key Concepts

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0. These equations have at most two real solutions and can be solved by various methods, including factoring, the quadratic formula, completing the square, or graphically finding the zeros where the function crosses the x-axis.

Graphing Calculators

Graphing calculators are tools designed to plot graphs of functions, which allow users to visualize equations and find approximate solutions by identifying intersection points or zeros of the function. They are especially useful for equations that do not factor neatly or when working with non-exact solutions.

Graphical Intersection/Zero Finding

This concept involves determining the points where a plotted function crosses the x-axis, representing the solutions or zeros of the equation. In the context of solving quadratic equations, these intersection points are the x-values that satisfy the equation, and graphing calculators facilitate the process by allowing users to trace or calculate these points accurately.

Rounding Approximations

Rounding approximations is the process of adjusting numerical results to a specified degree of precision, such as to the nearest hundredth. This is often necessary when using a graphical method to solve equations, as the outputs may be decimal approximations rather than exact values.

Transcript

00:01 All right, so we are looking now to be able to solve functions.

00:04 So again, for this one, we're using those same buttons, the y -equals, the calculate, and again, if you want to use the graph, you can use the graph or not.

00:13 So your very first step in is you're going to go into your y -equals button, and you're going to enter your equation.

00:19 Now, there's two ways to do this.

00:23 There's the textbook way, which shows you how to use the zero function, but i'm going to show you how to use the intersect function instead.

00:30 It will get you to the same answer.

00:32 You just have to do one more thing.

00:34 So in y1 i'm going to enter my equation.

00:37 So i'm going to type x squared plus x minus 6.

00:41 And in y2, i'm going to enter the answer i'm looking for.

00:46 So in this case, the answer i'm looking for is zero.

00:49 Now, this method will work for solving any answer of the function, not just zero, whereas the zero method only solves for zero.

00:59 So that's why i like this method just because you can use it for any type of answer.

01:05 It's not just stuck with zero.

01:07 From here, i have two graphs.

01:10 So i'm going to use something called the intersect key in my calculate menu.

01:15 So again, to get there, you go second trace to get into your calculate menu.

01:20 And the reason we use intersect is because we have two graphs.

01:24 So two graphs means you can use intersect.

01:29 If you don't have two graphs, you cannot use the intersect feature.

01:34 The whole point of the word intersect means that there's things that are crossing.

01:40 If you only have one, there's nothing to intersect.

01:45 So once we get that, you'll see your graph here, and you'll see a couple things.

01:51 So your graph is going to show up first.

01:52 That's important.

01:55 So when you get this graph, it's going to look a little light.

02:06 This give or take and that's going to be your y one graph there is going to be a second graph you won't see it unless you've got a difference kind of calculator that graphs in color if you do have the color graphing calculator you will see this one but it shows up right here along the x -axis because that's where y equals zero so you have one that shows up as your regular parabola and then one that shows up as x equals 0 so that one is your y2 so what it asks then is it's going to you'll see something in the top it might say y1 it might say y2 as long as it has one of them you're good so our y1 would be x squared plus x minus 6 it's already going to type that out for you you don't have to type it out and then it's going to say first curve question mark y question all you have to do is you have to make sure that your blinking arrow, you've got a little blinker on your graph, and you have a value somewhere along your graph for that.

03:34 So i can put it anywhere, and i'll see a graph value that shows up.

03:40 So you'll see a, you need to make sure there's an x, you need to make sure there's a y.

03:47 So, for example, i might see negative 4, positive 6.

03:51 Totally okay.

03:52 All we do, we hit enter.

03:56 Then it's going to ask you the second curve and you'll notice up here it has y equals zero as your equation.

04:04 That just means that we're graphing the second one now and you'll see again there's points there zero and zero.

04:13 So what i'll just do quickly is i'll quickly move this to all of my graphs so we can kind of see it on everything.

04:24 Infinite cloner.

04:39 There we go...

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