How do I do this one ?

Answer: fourth option -x² + 18x - 74

Explnation:

Since all the equations are parabolas, to find which one has a maximum at (9,7) you must verify two conditons:

1) the parabola opens downwards, and

2) the vertex is (9,7)

The first condtion means that the coefficient of the quadratic term is negative.

All the equations given meet that condition.

Therefore you have to find the vertex.

The vertex of a parabola is at the point where x = - b /(2a)

So, prove one by one.

Equation               b         a         x = -b/(2a)   

-x² -18x - 88        -18      -1         - 9 ⇒ not our equation (we aim to x = 9)

(jump to the last option)

-x² + 18x - 74        18      -1          9 ⇒ y = - (9)² + 18(9) - 74 = -81+162-74=7

Therefore, the last equation is the one.