Question

how can you determine the values of h and k from the graph shown? then write the function for the parabola.
the coordinates of the vertex are (k,h). from the graph, h = and k =
the coordinates of the vertex are (0,k), and the axis of symmetry is x = h. from the graph, h = and k =
write the function for the parabola
f(x) =
(type an expression using x as the variable )

Explanation:

To solve this, we use the vertex form of a parabola, \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex.

Step 1: Identify \( h \) and \( k \) from the vertex

The vertex’s coordinates are \((h, k)\). For example, if the vertex is at \((2, 3)\), then \( h = 2 \) and \( k = 3 \). (Assume the graph’s vertex is \((h, k)\) from visual inspection.)

Step 2: Write the parabola’s function

Substitute \( h \) and \( k \) into \( f(x) = a(x - h)^2 + k \). If \( a = 1 \) (for a standard parabola opening upward/downward with vertex \((h, k)\)), the function becomes \( f(x) = (x - h)^2 + k \).

Example (if vertex is \((0, 0)\)):

• \( h = 0 \), \( k = 0 \)
• Function: \( f(x) = (x - 0)^2 + 0 = x^2 \)

General Answer Structure:

• \( h = \boldsymbol{\text{[x-coordinate of vertex]}} \), \( k = \boldsymbol{\text{[y-coordinate of vertex]}} \)
• Function: \( f(x) = a(x - h)^2 + k \) (with \( a \) from the graph’s stretch/compression, or \( a = 1 \) if not specified).

(Note: Since the graph is not shown, substitute the actual vertex coordinates from the graph. For example, if the vertex is \((3, -2)\), then \( h = 3 \), \( k = -2 \), and \( f(x) = (x - 3)^2 - 2 \).)

Answer:

To solve this, we use the vertex form of a parabola, \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex.

Step 1: Identify \( h \) and \( k \) from the vertex

The vertex’s coordinates are \((h, k)\). For example, if the vertex is at \((2, 3)\), then \( h = 2 \) and \( k = 3 \). (Assume the graph’s vertex is \((h, k)\) from visual inspection.)

Step 2: Write the parabola’s function

Substitute \( h \) and \( k \) into \( f(x) = a(x - h)^2 + k \). If \( a = 1 \) (for a standard parabola opening upward/downward with vertex \((h, k)\)), the function becomes \( f(x) = (x - h)^2 + k \).

Example (if vertex is \((0, 0)\)):

• \( h = 0 \), \( k = 0 \)
• Function: \( f(x) = (x - 0)^2 + 0 = x^2 \)

General Answer Structure:

• \( h = \boldsymbol{\text{[x-coordinate of vertex]}} \), \( k = \boldsymbol{\text{[y-coordinate of vertex]}} \)
• Function: \( f(x) = a(x - h)^2 + k \) (with \( a \) from the graph’s stretch/compression, or \( a = 1 \) if not specified).

(Note: Since the graph is not shown, substitute the actual vertex coordinates from the graph. For example, if the vertex is \((3, -2)\), then \( h = 3 \), \( k = -2 \), and \( f(x) = (x - 3)^2 - 2 \).)