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General

General

Easy

Question

$y equals negative left parenthesis x minus 3 right parenthesis squared plus a$
In the equation above, a is a constant. The graph of the equation in the x y - plane is a parabola. Which of the following is true about the parabola?

its minimum occurs at (-3,a)
its minimum occurs at (3,a)
its minimum occurs at (-3,a)
its minimum occurs at (3,a)

hint Hint:

Hint:

A quadratic equation is an equation which has degree two.

The correct answer is: its minimum occurs at (-3,a)

Explanation:

We have given an equation . $y equals negative left parenthesis x minus 3 right parenthesis squared plus a$

We have to find the point, where the minimum value of function occurs.

Step 1 of 1:
We have given $y equals negative left parenthesis x minus 3 right parenthesis squared plus a$
Rewrite this equation,
$y equals a minus left parenthesis x minus 3 right parenthesis squared$
Here, we can see that $left parenthesis x minus 3 right parenthesis squared$ is always positive.
It means that any value of will give us value less than .
Therefore, we can say that the minimum value will be $negative straight infinity$ and it will occur at . $x equals straight infinity$
Now the maximum value occur $left parenthesis x minus 3 right parenthesis squared$ when
So,

At x=3
The value of function will be
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals negative left parenthesis 3 minus 3 right parenthesis squared plus a end cell row cell y equals negative 0 plus a end cell row cell y equals a end cell end table$
$T h e r e f o r e space space M a x i m u m space o c c u r s space a t space space.$
And Minimum occur at $left parenthesis straight infinity comma negative straight infinity right parenthesis$
And Minimum occur at $left parenthesis negative 3 comma a right parenthesis$

Hence, Option C is correct.

So,
At
The value of function will be

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