Suppose a parabola has vertex (6, -3) and also passes through the point (8, 5).
Write the equation of the parabola in vertex form.

Step-by-step explanation:

f(x) = a(x - h)² + k   ← vertex form of parabola equation with vertex (h, k)

So:

f(x) = a(x - 6)² + (-3)

f(x) = a(x - 6)² - 3      ←  vertex form of our parabola equation

Parabola goes through (8, 5) so if x=8 then f(x)=5

5 = a(8-6)² - 3

5 +3 = a(2)² - 3  +3

8 = 4a

a = 2

That means, the equation of a parabola with vertex (6, -3) and passing through the point (8, 5):

                                         f(x) = 2(x - 6)² - 3

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step-by-step explanation:

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guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: