Find constants a and b so that the minimum for the parabola f left-parenthesis x right-parenthesis equals x squared plus a x plus b is at the point left-parenthesis 6 comma 7 right-parenthesis. [hint: begin by finding the critical point in terms of a.]

and

Step-by-step explanation:

To find the constants, we need to replace the given point into the given quadratic function:

So, from the problem we have and . Then:

However, if we have a minimum at , the first derivate of the function must be zero at 6.

Now, we substitute this value in the previous expression:

Therefore, the values of the constants are and

the third picture

step-by-step explanation:

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