Test statement #1. f(x) = -0.3(x - 5)² + 5 This is the equation of a parabola with vertex at (5,5). Therefore the function is symmetric about x=5. The statement "The axis of symmetry is x=5" is TRUE.
Test statement #2. f(x) is defined for all real values of x. The statement "The domain is {x | x is a real nuber} is TRUE.
Test statement #3. As x -> -∞, f(x) -> -∞. f(5) = -0.3*(5-5)^2 + 5 = 5 Therefore f(x) is creasing over (-∞, 5) is TRUE.
Test statement #4. As x -> +∞, f(x) -> -∞. Therefore the curve is concave downward., and it has no minimum. The statement "The minimum is (5,5)" is False.
Test statement #5. The maximum value of f(x) occurs at the vertex because the curve is concave downward. The statement "The range is {y | y≥5}" is False.
Answer: The first three statements are True. The last two statements are False.
Okay, let me just make this a little clearer. Hopefully, this is what you meant:
A. y - 8 = -4(x + 4) B. y - 8 = 4(x + 4) C. y + 8 = 4(x - 4) D. y + 8 = -4(x - 4)
--
This can also be written as y2 - y1 = m(x2 - x1).
Your M is your slope.
Both A and D have their m as a negative 4. Because you are looking for a positive slope, immediately cancel those answers.
* note that you could have also put them in a more standard form and discovered m which is the x in bx.
Now, you are looking for an equation that contains (4,-8).
Because it is written as y2-y1, your y's are actually points if you were to find another slope or something. This part is a bit hard to explain, but -8 is only found in the y coordinate place in answer B. Your answer would be B. For more explanation on that, there's this great site called coolmath.com and if you search for finding the equation of two points, it explains it much better on there, but I would not want to plagiarize.
