Problem

For vertex-form quadratic \(f(x)=2(x-3)^{2}+5\), identify \(a\),\(h\),\(k\), vertex, symmetry axis, opening, width/stretch-compression match, and extremum.

Unannotated parabola without a vertex marker or feature labels.

Big Picture

What this problem is really about

Vertex form packages the graph’s key features into three parameters. We’ll compare the expression with a times the quantity x minus h squared plus k, read the inside sign carefully, and use h and k for the vertex and axis while the sign and magnitude of a determine opening, width, and whether the extremum is a minimum or maximum.

Answer choices

Choose your path.

Preview only

a=2,h=-3,k=5; vertex=(-3,5); axis=x=-3; opening=up; scale=vertical stretch factor2/narrower; extremum=minimum5

a=2,h=3,k=5; vertex=(3,5); axis=x=3; opening=up; scale=vertical stretch factor2/narrower than y=x²; extremum=minimum5

a=-2,h=3,k=5; vertex=(3,5); axis=x=3; opening=down; scale=vertical stretch factor2/narrower; extremum=maximum5

a=2,h=3,k=5; vertex=(3,5); axis=x=3; opening=up; scale=vertical compression factor1/2/wider than y=x²; extremum=minimum5

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

For vertex-form quadratic \(f(x)=2(x-3)^{2}+5\), identify \(a\),\(h\),\(k\), vertex, symmetry axis, opening, width/stretch-compression match, and extremum.

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.