Answer:
2nd one
Step-by-step explanation:
(x*x*x*x*x*x*x*x*x)
or x^9
It can have however many x intercepts it wants,
<span>BUT, to be a function it must pass the vertical line test. </span>
<span>this means you have to look at the graph and see if a vertical line drawn anywhere hits the graph more than once. </span>
<span>if it hits it more than once, it is NOT a function.
</span>
An example is a polynomial function to the infinite degree. That is
f(x) = lim (n --> infinity) [ x^n]
but only 1 y intercept (vertical line test remember)
Y = -(1/2)(x-2)² +8
Re write it in standard form:
(y-8) = -1/2(x-2)² ↔ (y-k) = a(x-h)²
This parabola open downward (a = -1/2 <0), with a maximum shown in vertex
The vertex is (h , k) → Vertex(2 , 8)
focus(h, k +c )
a = 1/4c → -1/2 = 1/4c → c = -1/2, hence focus(2, 8-1/2) →focus(2,15/2)
Latus rectum: y-value = 15/2
Replace in the equation y with 15/2→→15/2 = -1/2(x-2)² + 8
Or -1/2(x-2)² +8 -15/2 = 0
Solving this quadratic equation gives x' = 3 and x" = 2, then
Latus rectum = 5
Answer: h(x) = -1200x^2 + 1950x + 4950
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Work Shown:
f(x) = revenue from the north
f(x) = -750x^2 + 1500x + 2250
g(x) = revenue from the south
g(x) = -450x^2 + 450x + 2700
h(x) = total revenue, ie add the two revenues
h(x) = f(x) + g(x)
h(x) = (-750x^2+1500x+2250)+(-450x^2+450x+2700)
h(x) = -1200x^2 + 1950x + 4950
