Find the vertex of the parabola whose equation is y = -2x2 + 8x - 5. (2, 3) (2, 19) (2, 27)

The vertex is the point where the graph is horizontal, which you can find by setting the first derivative to zero.

derivative: -4x + 8 = 0 => x=2
fill it in in the equation:

y=-2*2² + 8*2 - 5 = 3

So the answer is the point (2,3)

In order to do this you have to put it into vertex form, which is achieved by completing the square.  Start out by setting it equal to 0. .  Next, move the 5 over to the other side of the equals sign. .  In order to complete the square, the rule is that the leading coefficient on the squared term is a positive 1.  Ours is a -2, so we have to factor it out. .  Complete the square by taking half the linear term (the linear term is 4 now), square it and add it to both sides.  Half of 4 is 2, and 2 squared is 4, so we will add it in.  HOWEVER, when you add it into the parenthesis on the left, you still have that -2 hanging out front, so what you really have added in is -2(4) which is -8.  Here's what we have now so far: which simplifies to .  The next step is to create the perfect square binomial we formed during this process on the left, which gives us .  Move the -3 back over to the other side by addition and you get .  This tells us that our vertex is (2, 3)

the image of (6, 9) under a dilation is (4, 6). the scale factor is

b. 2/3