analytic geometry Quadratic Functions: Factored Form Assignment

Which graph represents the function f(x) = (x - 3)2?

graph C

Graph the function f(x) = (x + 1)(x - 5). Use the drop-down menus to complete the steps needed to graph the function. Identify the x-intercepts: (-1, 0) and (5, 0) Find the midpoint between the intercepts: (2, 0) Find the vertex: Find the y-intercept: Plot another point, then draw the graph.

(2,-9) (0,-5)

Explain how you could write a quadratic function in factored form that would have a vertex with an x-coordinate of 3 and two distinct roots.

sample response : The vertex is on the axis of symmetry, so the axis of symmetry is x = 3. Find any two x-intercepts that have the equivalent distance from the axis of symmetry. Use those x-intercepts to write factors of the function by subtracting their values from x. For example, 2 and 4 are each 1 unit from x = 3, so f(x) = (x - 2)(x - 4) is a possible function.

Mr. Walker gave his class the function f(x) = (x + 3)(x + 5). Four students made a claim about the function. Each student's claim is below. Jeremiah: The y-intercept is at (15, 0). Lindsay: The x-intercepts are at (-3, 0) and (5, 0). Stephen: The vertex is at (-4, -1). Alexis: The midpoint between the x-intercepts is at (4, 0). Which student's claim about the function is correct? The claim by is correct.

Stephen

What is the vertex of the quadratic function f(x) = (x - 8)(x - 2)? (,)

(5,-9)

The graph of the function f(x) = -(x + 1)2 is shown. Use the drop-down menus to describe the key aspects of the function. The vertex is the . The function is positive . The function is decreasing . The domain of the function is . The range of the function is .

1.) maximum value 2.) for no values of x 3,) when x > -1 4.) all real numbers 5.) all numbers less than or equal to 0

Which point is an x-intercept of the quadratic function f(x) = (x - 4)(x + 2)? (-4, 0) (-2, 0) (0, 2) (4, -2)

B (-2, 0)

The graph of the function f(x) = (x + 6)(x + 2) is shown. Which statements describe the graph? Check all that apply. The vertex is the maximum value. The axis of symmetry is x = -4. The domain is all real numbers. The function is increasing over (-∞, -4). The function is negative over (-6, -2).

B The axis of symmetry is x = -4. C The domain is all real numbers. E The domain is all real numbers.

Zander was given two functions: the one represented by the graph and the function f(x) = (x + 4)2. What can he conclude about the two functions? They have the same vertex. They have one x-intercept that is the same. They have the same y-intercept. They have the same range.

C They have the same y-intercept.

Which function has a vertex at (2, -9)? f(x) = -(x - 3)2 f(x) = (x + 8)2 f(x) = (x - 5)(x + 1) f(x) = -(x - 1)(x - 5)

C f(x) = (x - 5)(x + 1)