Mathematics High School

which of the following quadratic will have a maximum value at x=3
(A) y=x^2-6x+19
(B) y=-4x^2+24x-21
(C) y=-2x^2+20x-49
(D) y=2x^2-3x+7

Answers

Answer 1

The x = 3 the quadratic equation D) y = 2x² -3x +7 will have maximum value.

The maximum and minimum values of a function:

The maximum and minimum values are the highest and lowest values that a function can reach over a particular domain.

For example, in a quadratic function, the maximum or minimum value is the highest or lowest point on the graph, respectively.

If a function has a maximum value, it means that the function reaches its highest point at a certain value of x.

On the other hand, if a function has a minimum value, it means that the function reaches its lowest point at a certain value of x.

Here we have

(A) y = x²-6x +19  

At x = 3

y = (3)² - 6(3) + 19  

= 9 - 18 + 19 = 10

(B) y = -4x²+24x -21

At x = 3

y = -4 (3)² + 24(3) - 21

= - 4(9) + 72 - 21

= 15

(C) y= -2x² +20x -49

At x = 3

y = - 2 (3)² + 20(3) - 49

= - 18 + 60 - 49

= - 7

(D) y = 2x² -3x +7    

At x = 3

y = 2(3)³ - 3(3) + 7

= 18 - 9 + 7

= 16

Therefore,

The x = 3 the quadratic equation D) y = 2x² -3x +7 will have maximum value.

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