In this problem, uh There is a given function expressed as f of X is equal to a X cubed. Just be X squared the C express D in a given condition says that this specific function passes through the following points P Q R N. S. So they know that if a given function passes through a given point, then we know that plugging in the X and y coordinates of that point to the function. We should we surely know that it will satisfy the equation. Now the end goal for this problem is to identify what the value of A, B, C, and D. So that we can find out what is the actual coefficients of the variables of the variable X. In this given function. Perfect. So for us to be able to do that, what what we first want to do is to plug in the X and Y coordinates of this point, speak U R N. S. The given function. So let's start with point P. So plugging in point T. To the function. We have zero comma fourth they know that the first coordinated ever since X. And the second coordinate represents the F. Of X. Or the Y. Okay so plugging in P. Accordingly to be on the given function will have four Is equal to eight times 0 Cube. Just feed them squared The seat and zero plus d. So both abc and yeah A. B and C. Are all gonna be zero because it's being multiplied to a zero value. That being said will end up having the is about for this one and this is the first variable we were able to calculate now for cues plugging in the values of Q. To the function will have two is equal to eight times 1. two Just be times one squared The see there's one. The steel We have two is equal to a. Just be the sea Last four. We know the value of for it we know the value of the it's equal to four. So we can plug in for um for the and this should give us a simplified equation and speed. Just be the C. Is equal to negative two. And it's called it equation number one. All right now plugging in point are which is negative one comma 10 will have 10 is equal to eight times negative one Cube. Let's be times negative point squared, Proceed as negative one with me Teresa. It's a bit messy. First D. Which is equal to pork. So we'll end up having six right here negative A. Because B minus Or let me just try to ride it this way. Let me release that one. Instead I negative a less B minus C. Is equal to six. And let's call it the equation number. Uh huh. I'm plugging in the last point point. Is It coordinates to -2 will have -2 is equal to eight times to kill just be banks. Two squared. See time's too this form The is equal to four. Okay. So we'll end up having excuse me. We end up having A. Does four B. The Stasi Sequencing to -6. Right? And let's call it equation number. So we have now three equations with three unknown variables A. B. C. This is now a system of linear equation and we have a bunch of method to solve this and I will try to solve this using elimination method. So the first thing I wanted to eliminate is variable C eliminate. See an equation one and two. And how are am I going to do that? So I will simply just add equation one. Nothing erased this one. I will simply add equation one with equation too. No that equation one is a plus b. The C is equal to negative and the question number two is negative. A. Just B minus C. C. Cold six. And they ignored by looking at it. It seems like if I will add this equation, I can actually eliminate two variables. So here let me reach this a little bit and let's say eliminate A. And C. in equation one and 2. So adding these two equations, we can cancel out A, cancel out, see and end up having to be is equal to positive four, Dividing both sides by two, will end up having B. is equal to. But this is the second variable we were able to calculate in this problem now we still need to find out what A. In C. R. So how are we going to do that? So what I am thinking is to um Maybe we can eliminate we can eliminate C. In equation one 10 3. And how am I going to do that? I will just multiply the equation number one by two. And then Sandra. Oh asian number two times equation one minus equation three. So let's try to do that two times equation one. Which is A plus B plus C equals negative tomb minus equation number three which is eight A. Does four B. Just to see is equal to -6. Now let's try to simplify the first equation. That should be equal to two a. That's to be just to see Equal to -4. Mine is the second equation equation number three 88 plus four B. To C. Equal to negative six. All right Drafting each term. So to -8 we have negative 68 2 4. We have negative to be and to c minus to see that canceled out. And negative four minus negative six. That should be positive too. Now from here, from the equation we were able to generate here. They thought that we can actually sold for a already why? Because we already know what the value of B. S And B is equal to two. So I'm plugging in the value of be here in this equation and that gives me the negative six A minus four is supposed to do Or -6 Day is equal to positive six, dividing both sides by -6 will have a sequel to Groups. Should be -1. This is not the value of pain. The only variable left and solve is variable C. And how am I going to soil for variable. See now you can pick any equation that we have written previously to solve for C. And let's say I wanted to use equation number one. So from equation number one at first A plus B plus C is about the negative to I know what is its negative one? I know what B is. It's positive to. So then I can solve for C. So this is one Plus C is equal to negative tool. So C. is simply equal to -3. All right. So for the question, we wanted to identify the actual coefficients of dysfunction and we were able to find out what A. B. C. And D. Here and um just to write the equation or dysfunction with its actual value. This should be equal to um Ever met equals a negative X. Q. These two plus two X squared See you think they read -3 x. And these four best four. So that should be the actual equation of this given function.