Followingisa statementof a theoremwhichcan beproven usingthequadratic formula. For this theorem, a, b, and c are real numbers. Theorem If f is a quadratic function of the form f .x/ D ax2 Cbx Cc and ac < 0, then the function f has two x-intercepts. Using only this theorem, what can be concluded about the functions given by the following formulas(a) g (x) = -8x^2 + 5x - 2 (b) h (x) = -(1/3)x^2 + 3x (c) k (x) = 8x^2 - 5x - 7 (d) j (x) = -(71/99)x^2 + 210 (e) f (x) = 4x^2 - 3x + 7 (f) F (x) = -x^4 + x^3 + 9

We have the following theorem:

If f is a quadratic function of the form and , then the function f has two x-intercepts.

(a)

For this function a = -8 and c = -2, then is greater than zero. Therefore, we cannot conclude anything.

(b)

For this function a = -8 and we don't know the value of c. Therefore, we cannot conclude anything.

(c)

For this function a = 8 and c = -7, then is less than zero. Therefore, we can conclude that the function k has two x-intercepts.

(d)

For this function a = and c = 210, then is less than zero. Therefore, we can conclude that the function k has two x-intercepts.

(e)

For this function a = 4 and c = 7, then is greater than zero. Therefore, we cannot conclude anything.

(f)

We cannot conclude anything because this is not a quadratic function.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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step-by-step explanation: yes