which of the following equations represents a parabola that

ar Quadratic and Exponential Models SUBMIT ANSWER NEXT Question 4 of 10 Multiple Choice: Please select the best answer and click \"submit.\" Which of the following equations represents a parabola that opens down and has a vertex with a positive x-value? O A- y -3x +22x +8 B. y -6x +14x-12 C. y -2x -12x-18 o D. y 2x2 -10x+8

Solution

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Of the given options, since coeffiecent of x^2 is positive only for option a and c therefore only these 2 paeabola shall be opening downwards

a) y = -3x^2 + 22x + 8

For vertex of parabla let us differenciate w.r.t. x

dy/dx = -6x + 22 = 0

x = 22/6 = 11/3

y = -3(11/3)^2 + 22(11/3) + 8

= 48.33

It clearly shows option A has vertext with positive x value. Hence equation with positive vertex and which opens downwards is parabola in option A.

For option C

y =-2x^2 - 12x - 18

Differenciating w.r.t. x

dy/dx = -4x -12 = 0

x = -3

=>

y =-2(-3)^2 - 12(-3) - 18

= -18 +36 - 18

=0

Clearly this parabola in option C has a vertex with negative x value, hecne it is not a correct option.