So if x minus six is equal to zero, then that would make this equation true. Well one half is one-half, it's not going to be equal to zero. If I have the product of multiple things and it needs to be equal to zero, the only way that's going to happen is if one or more of these things are going to be equal to zero. One half times x minus six, times x plus two is equal to zero. Have to figure out when, if we want to know when y equals zero, then we have to solve for when does this expression equal zero? So let's just solve the equation. When does y equal zero? Well to solve that we just To get the general shape of this curve which is And then from that, we'llĪctually be able to find the coordinates of the vertex and we're going to be able Times that we're intersecting the x-axis. When does y equal zero? Which are going to be the And the form that it's in, it's in factored form already, it makes it pretty straightforward for us to recognize So let's see if we can find out where this intersects the x-axis. Now a parabola you might remember can intersect the x-axis multiple times. I'm going to get x-squared, plus something, plus something else. Six times x plus two, I'm going to get a quadratic. The key realization here withoutĮven having to do the math is if I multiply this out, if I multiplied x minus We can get the essence of this graph withoutĭoing that much work. Try to connect the curve that connects all of those dots. Try out a bunch of x values and a bunch of y values and There's many different ways that you could attempt to graph it. So like always, pause this video and take out some graph paper or even try to do it onĪ regular piece of paper and see if you can graph this equation. To graph the equation y is equal to one-half times x minus six times x plus two.
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