Question

Which of the following points denotes the highest or lowest point of quadratic function y=a(x−h)²+k?

A) Highest point: (h,k)
B) Lowest point: (h,k)
C) Highest point: (h,-k)
D) Lowest point: (h,−k)

Answer 1

The vertex (h, k) of the quadratic function y = a(x-h)² + k is the lowest point if 'a' is positive, making the correct answer B, and it is the highest point if 'a' is negative, corresponding to answer A.

Step-by-step explanation:

The point that denotes the highest or lowest point of a quadratic function in vertex form y = a(x-h)² + k is known as the vertex of the parabola. If the coefficient a is positive, the parabola opens upwards, and the vertex represents the lowest point on the graph.

Conversely, if a is negative, the parabola opens downwards, and the vertex is the highest point on the graph. Hence, the correct answers are:

• B) Lowest point: (h, k) when a is positive.
• A) Highest point: (h, k) when a is negative.