Question

Please help and explain.

Answer 1

Explanation:

Vertex form of a quadratic function is given by y = a(x - h)² + k

where

1) 'a' determines if parabola is stretched or compressed.

   If a > 1 then graph is stretched by a factor of a.

   If 0 < a < 1, then graph is compressed by a factor of a.

2) If a > 0 then graph opens upwards with a happy face. (minimum)

3) If a < 0 then graph opens downwards with a sad face. (maximum)

4) (h, k) is the vertex point

5) The axis of symmetry is x = h

While solving for y = 1(x - 4)² + 3

Identify following's:

Vertex: (h, k) = (4, 3)

Axis of symmetry: x = 4

Max/Min: As here a > 0, Minimum (4, 3)

Stretch/compression: a = 1, the graph is stretched by a factor of 1.

Direction of opening: As a > 0, the graph opens upwards.