Question

question 22/35
the function ( f(x) = x^2 ) is the starting point for sketching the graph of any parabola. the vertex form of a parabola is written as ( f(x) = a(x - h)^2 + k ). match each part of the equation with its appropriate role in the function.
( a )
( k )
( h )
drag & drop the answer
horizontal shift (left/right)
steepness (wider/narrow) and direction (opening up/opening down)
vertical shift (up/down)

Explanation:

Step1: Identify role of a

In \(f(x)=a(x-h)^2+k\), \(a\) controls stretch/shrink and direction (sign of \(a\) determines up/down opening).

Step2: Identify role of k

\(k\) shifts the parabola vertically (up if positive, down if negative).

Step3: Identify role of h

\(h\) shifts the parabola horizontally (opposite to sign: \(h>0\) shifts left, \(h<0\) shifts right).

Answer:

a - Stretch/Shrink and Direction (opening upward/downward)
k - Vertical shift (up/down)
h - Horizontal shift (left/right)