Question 147711
1. y=mx+b where m is the slope and b is the y-intercept (what y is when x is zero).  So y=-2x+b. To find b, you know that the slope is rise/run or -2/1.  So take the point (-1,6) and add 1 to x and subtract 2 from y. You get {{{0,4}}}. So the y-intercept is 4. So {{{y=-2x+4}}}.


2. (2x-7)(x+4)=0. Just take each expression separately and set each one equal to zero.  what minus seven equals zero? Seven. So you know 2x=7.  So x there is 7/2.  What plus four equals zero? x=-4 there. So the solutions for this equation are x=7/2;-4.


3.find the vertex of f(x)=3x^2-6x+8. vertex: the value of y that does not repeat.  To get this, plug in a few consecutive values of x and see which one does not repeat an answer.  That would be the vertex.  In this case, I will let you know that it is at (1,5). Because:
*[invoke quadratic "x", 3, -6, 8]

5 is the only y value that does not repeat.


4. find the y-intercept of the cubic f(x)=(x-2)(x+1)(x-3). y=f(x), so that means find f(0), because the y-intercept is what y is when x is 0.  So plug in 0 and get {{{f(0)=(0-2)(0+1)(0-3)}}}. Or {{{f(0)=(-2)(1)(-3)}}}. Multiply it all out and get {{{6}}}.  So the y-intercept is 6.