![]() ![]() I get 9, so 2 9 is going to be my vertex. I just need to plug 2 into my function, and I get 1+2 or 3, 5-2 times 3. So the vertex is somewhere on this line x=2. So that's going to be 4 over 2 which is 2. So I can just average the two x intercept values -1 and 5 and I'll get the x value of the vertex. ![]() Remember if you have the x intercepts, the vertex is going to be exactly halfway between them. And also it's pretty easy to find the vertex. We get that by plugging x=0 in so we get one times 5, 5. ![]() And since it's easy enough to find, let's find the y intercept. The x intercept is going to be -1 0 and 5 0, so here's -1 0, here's 5 0. First thing I like to do is to plot the intercepts. Now first of all, quadratics are really easy to graph. Well anyway let's graph this quadratic function and see what the restricted domain does to the graph. You want to make sure that that always ends up positive or that the input is always positive something like that. We would make it a restriction like this if we just wanted to keep it to a certain interval of numbers like between 0 and 5 and this is often done when you're doing mathematical modelling, you're trying to make the function for example model revenue. Now normally a quadratic function is defined for all real numbers. I have a function, a Quadratic function the quantity 1+x times the quantity 5-x, restricted to the domain x is between 0 and 5. I want to talk about domain restrictions. ![]()
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