solving systems of linear and quadratic equations

SOLVING SYSTEMS OF LINEAR AND QUADRATIC EQUATIONS HOW TO
SOLVING SYSTEMS OF LINEAR AND QUADRATIC EQUATIONS PLUS

But once again, under time pressure I wouldn't have necessarily gone through to this extra length.What you call the turning point we call a maximum or a minimum point, which as you observed is where the graph changes direction or turns. So we took a little extra time to make sure that we feel good about this.

SOLVING SYSTEMS OF LINEAR AND QUADRATIC EQUATIONS PLUS

This on the left hand side is gonna be negative six plus six. And when Y is negative three, two times negative three And that's what we saw right over here with when Y is five, X is 16. So when Y is equal to five, you have 10 plus six. Because we have two times five plus six is equal to X. Three, X is equal to zero, you can go back and substitute

But if you want to go back and feel good that when Y equals five, X equals 16 and Y equals negative So if I was under a time pressure, I would just stop there and I would move on to the next question 'cause I feel good about this choice. That says X is equal to five and X is equal to negative three.

This one puts the fiveĪnd the negative three in for the X-coordinate. Immediately pretty good about this choice right over here. This one is Y is equal to five and Y is equal to negative three. So Y equals five and YĮquals negative three. To trick us a little bit because you know we have this number five and negative three, it's like hey, maybe this oneīut this isn't Y equals five, this is X equals five. And these first two don'tĮven have two choices and but this one right over here, this one is actually trying Try to solve for the Xs or we can immediately look at our choices and say well are either of these choices have Y equals five and Three would make this zero, which would make thisĮntire expression zero, so this is also a solution. Would make one of these, Y equals five would make this zero, which would make theĮntire expression zero, so this is a solution. This one equal to zero? Well Y would be equal to negative three. So the solutions are gonna be how do you make this one equal zero? Well Y would be equal to five. Product of two things that are equal to zero that means that you could get this to equal zero by making one or both

SOLVING SYSTEMS OF LINEAR AND QUADRATIC EQUATIONS HOW TO

But we now know how to factor, this is gonna be zero isĮqual to, we can write this as Y minus five times Y plus three. Do a search on Kahn Academy for factoring quadratic expressions. And if what I'm doing right now looks a little bit like voodoo to you, I encourage you to reviewįactoring quadratic expressions on Kahn Academy. Product is negative 15 their sum is negative two. So it's gonna be negative five and three. Well if the sum is negative that means that the negative number has Numbers three and five, either negative three, positive five or positive three, negative five jump out and whose sum is negative two. Would do that is first of all kind of think of two numbers Quadratic right over here, we could factor this quadratic, we could factor this quadratic expression. And now to solve for the Ys that would satisfy this Write it the other way, Y squared, let me write the minus 2y minus 15. Side you're gonna have Y squared minus 15 minus, actually let me And then on the left hand side we're gonna be left with zero. And we could subtract six from both sides.

So if 2y plus six is equal to Y squared minus nine. Then can solve for Y, the Y of a solution to this system. Well this one actually canīe solved with substitution because 2y plus six needs to be equal to X but then we also that X isĮqual to Y squared minus nine. The following represents all solutions X comma Y to the system of equations shown below? This is an interesting system of equations because this is a linearĮquation, this first one, but the second one is nonlinear.

Solving systems of linear and quadratic equations