For each equation, (a) give a table with at least three ordered p...

Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.

y = x²

Accepted Answer

Welcome back everyone. In this problem, we want to sketch the graph of Y equals four X squared by using a table of ordered pairs on our coordinate grid. Our domain for X ranges from negative 5 to 5 and the range goes from negative 10 to 50. Now we're sketching a quadratic graph and recall that for a quadratic graph in the form Y equals A X squared, then our graph is going to form a parabola, a parabola at which its vertex or, or its minimum point would be at the origin. So that's what we expect our graph to look like. The thing is though for our domain is from negative 5 to 5 and we might not use all those points. So first, let's see what's an appropriate domain to use for the graph we have to sketch on, we can do that by just let's brainstorm some values, right? So let's say when X equals negative five, what would the value of Y be? Well, negative five squared is 25 and 25 multiplied by four is 100. That Y value isn't on our graph. So we may not need X being negative five or five when X equals four, well, four squared equals 16 and 16 multiplied by four is 24. So we may not need four, either bolt when X equals three. Well, that one looks a little more promising because if I were to put a table here of my values when X equals three, then Y equals four multiplied by three squared which is four multiplied by nine, which is 36. And that value is less than 50. It fits on our graph. So we can plot the value of 36 in order to find what our graph would look like on the grid we have. So that's an appropriate value. Therefore, I'm going to use the domain for X being between negative three to positive three. So that's negative three, negative two, negative 10123. So now I just need to figure out the rest of Y values so that we can plot our graph. Now when X equals negative three, Y equals four multiplied by negative three squared, that would be four multiplied by nine because negative three squared is nine and four multiplied by nine equals 36. When X equals negative two, Y equals four multiplied by negative two squared, ne negative two squared is positive four and four multiplied by four equals 16. When X equals negative one, Y equals four multiplied by a negative one squared. Thus four multiplied by a positive one which is four when X equals zero, Y equals four multiplied by zero squared, which we know would give us zero. No, we know that a Parabola is symmetric. In other words, on the other side of the Parabola, it would be the same values as on the mirror or, or on its image. So that means when X equals one, we'd get the same value as when X equals negative one. So when X equals one, Y equals four, when X equals two, Y equals 16. And like we had figured out at first, when X equals three, Y equals 36 know that we have all our points, we can go ahead and plot and then draw our curve. So an X is negative three. So let me just identify these on our grid here, negative one, negative two, negative three. And we have 12 and three. I'll just put in the four for fun. When X equals negative three, Y equals 36 when X equals negative two, Y equals 16, when X equals negative one, Y equals four, when X equals zero, Y equals zero, then when X is one, Y is four, X is two, Y is 16 and we have 3 36 already on our graph know that we have these values, we can go ahead and plot our Parabola. So our Parabola is going to look something like this. I hope I draw my curve really neatly. I have a good feeling you can do better than me, but that would be our graph of Y equals four X squared. Thanks a lot for watching everyone. I hope this video helped.

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4. y = x²

Key Concepts

Quadratic Functions

Ordered Pairs

Graphing Techniques

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