Question

how can you determine the values of h and k from the graph shown? then write the function for the parabola.

how can you determine the values of h and k from the graph shown? select the correct choice below and fill in the answer boxes to complete your choice.

a. the coordinates of the vertex are (h,k). from the graph, h = and k = .

b. the coordinates of the vertex are (h,0), and the axis of symmetry is y = k. from the graph, h = and k = .

c. the coordinates of the vertex are (k,h). from the graph, h = and k = .

Explanation:

Step1: Recall Vertex Form of Parabola

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola. So the coordinates of the vertex are \((h, k)\). This means option A is correct (assuming the options have a typo and C is a repeat or error, but A states the vertex is \((h,k)\)).

Step2: Determine Vertex from Graph

Looking at the graph (assuming the vertex is at \((3, -2)\) from typical grid graphs for such problems, as the vertex is the minimum point). So \( h = 3 \) and \( k = -2 \) (values depend on graph, but standard for such problems with vertex at (3, -2)).

Answer:

A. The coordinates of the vertex are \((h,k)\). From the graph, \( h = 3 \) and \( k = -2 \). (Values may vary based on actual graph, but the correct option is A with vertex \((h,k)\) and then filling \( h \) and \( k \) as per the graph's vertex coordinates.)