Question

These 3 equations all describe the same quadratic function. What are the coordinates of the following points on the graph of the function? From which equation is each point most easily determined?

y = (x - 5) (x + 1)

y = x^2 - 4x - 5

y = (x - 2) ^2 - 9

X-intercept, what are the points, the equation, and explanation why that equation is the one from which the x-intercepts are most easily determined?

Answer 1

the form y = (x - 5) (x + 1)
yields the x-intercepts the fastest
simply set each bracket = zero and solve for x
In most cases you can do this mentally
e.g. x = 5 and x = -1

y = (x - 2) ^2 - 9 yields the vertex by "just looking at it"
the vertex is (2,-9)

y = x^2 - 4x - 5 , no real advantage, simply the easiest to type