ALGEBRA2AlgebraQuestion 1If f(t)=at−a , then to get f(at)we replace t with at as follows.f(at)=aat−a=aat−a×tt=ata−at=a(t)a(1−t)=t1−tQuestion 2To get the steepness of a line, we find the change in the y-coordinate as a ratio of the change in the x-coordinate. That is, if we have two points on a line denoted by the coordinates(t1,y1)∧(t2,y2), the steepness a is defined by, a=y2−y1t2−t1If we let y=b, then the line cuts the y-0axis at a point with the co-ordinates (0,b). Then, from the from figure 1 attached, if the two points on the line are (t,y)∧(0,b) the equation of the line can be derived as shown.a=y2−y1t2−t1=y−bx−0=y−bxa=y−bxMaking ythesubjectoftheformulayieldsy=at+b
ALGEBRA3Question 3Part aA variable is the parameter with an unknown value in an equation. That is, parameter x in the equationax2+bx+c=0. On the other hand, a constant is a value that does not change in an equation. That is, its value is known. If we want to solve for the unknown variable in a quadratic equation, we write the equation in the form ax2+bx+c=0. Then, the corresponding values of a, b, and c are plugged in the quadratic formula to solve for the unknown.Part bYes, it works. If we write y=ax2 in the form ax2+bx+c=0, we get ax2+0x+0=0 which means that a and c are zero. Then we can insert the values in the quadratic formula to solve for the unknown.Question 4
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