Question

How does the equation of a quadratic function in vertex form highlight key features of the function’s graph?

Answer 1

From the vertex form ()=(−)+ , you can find the vertex (,) and see whether the parabola opens upward (if > ) or downward (if < ). From a graph, you can read the coordinates of the vertex and substitute into the vertex form. With the coordinates of one other point, you can solve the equation to find a and write the equation of the quadratic function in vertex form.

Answer 2

9514 1404 393

Step-by-step explanation:

Vertex form of a quadratic can be written as ...

a(x -h)² +k = 0 . . . . . . vertex (h, k); scale factor 'a'

First of all, it highlights the vertex (x, y) = (h, k), which is the extreme maximum or minimum of the function. That also tells you the axis of symmetry, (x = h).

Vertex form also shows you the vertical scale factor. The sign of that tells you whether the graph opens upward (positive) or downward (negative). The numerical value of it tells you the vertical distance from the vertex to points ±1 unit either side of the vertex.

The roots of the quadratic will be ...

x = h ±√(-k/a)

These will be complex if the graph does not intersect the x-axis.