Question

Tell whether the graph opens upwards or downward and whether the parabola has a maximum or minimum y=-x2-7x+18

Answer 1

Downwards, maximum

Explanation:

In a quadratic function - one of the form
`y=ax^2+bx+c` where a, b, and c are all constant - the direction of the parabola is determined by a. If a is positive, the parabola opens upward - it has no maximum, since it shoots up infinitely in the positive y direction, but it does have a minimum; if you dropped a marble inside the parabola, it's the point where that marble would eventually rest. If a is negative, our parabola opens in the negative y direction, and the graph has a maximum. To use the marble analogy, the maximum is the one point where the marble won't roll off the sides of the graph.

Our function has a = -1, so it opens downward and has a maximum point.