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What are the features of the parabola modeled by the equation f(x) = x2 - 114x ?
Include
domain, range, intercepts, maxima or minima, intervals of increase and decrease in your answer.

Sagot :

Answer:

Answers are in bold type

Step-by-step explanation:

f(x) = [tex]x^{2} -144x[/tex]

The parabola opens up, so has a minimum at the vertex.

Let (h, k) be the vertex

h = -b/2a = - (-144)/2(1) = 57

k = 57^2 - 144(57) = 3249 - 6498 = -3249

Therefore, the vertex is (57, -3249)

The minimum value is -3249

The domain is the set of real numbers.  

The  range = {y | y ≥ -3249}

The function decreases when -∞ < x < 57  and increases when 57 > x > ∞

The x - intercepts:  [tex]x^{2} -144x[/tex] = 0

                                x(x - 114x) = 0

                                x = 0 or x = 114

x-intercepts are (0, 0) and (0, 114)

When x = 0, then we get the y-intercept.  So, 0^2 - 114(0) = 0

y-intercept is (0, 0)

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