Question

Which of the following equations has a maximum at (9,7)

A. y = -12 + 141 - 40
B. y = -12 -180 -88
c. y = -12 + 18a - 74
D.y = –12 – 14. – 58

Answer 1

C

Explanation:

y = a(x - h)² + k

Since it's a maximum turning point:

a < 0

From the options available, a = -1

y = -(x - 9)² + 7

y = -(x² - 18x + 81) + 7

y = -x² + 18x - 81 + 7

y = -x² + 18x - 74

Answer 2

Explanation:

Answer:

option C ⇒ C) y = -x² + 18x - 74

Explanation:

The given options are:

A) y = -x² + 14x - 40

B) y = -x² - 18x - 88

C) y = -x² + 18x - 74

D) y = -x² - 14x - 58

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The general equation of the parabola has the form:

y = f(x) = ax² + bx + c

The vertex of the parabola has the coordinates (h , k)

where h =
`(-b)/(2a)`

and k = f(h) = f(
`(-b)/(2a)`)

Check option A: a = -1 , b = 14 ⇒ (h,k) = (7, f(7) ) = (7 , 9)

Check option B: a = -1 , b = -18 ⇒ (h,k) = (-9, f(-9) ) = (-9,-7)

Check option C: a = -1 , b = 18 ⇒ (h,k) = (9, f(9) ) = (9,7)

Check option D: a = -1 , b = -14 ⇒ (h,k) = (-7, f(7) ) = (-7,-9)

So the equation which has a maximum at (9,7) ⇒ y = -x² + 18x - 74

So, the correct answer is option C