Quadratic Functions: Vertex Form — Unit test Answers

The graph of the function f(x) = –(x + 3)(x – 1) is shown below.

Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6?

Which function in vertex form is equivalent to f(x) = x2 + x +1?

According to one company’s profit model, the company has a profit of 0 when 10 units are sold and a maximum profit of $18,050 when 105 units are sold. What is the function that represents this company’s profit f(x) depending on the number of items sold, x?

The function f(x) = –(x – 3)2 + 9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?

Which function has an axis of symmetry of x = −2?

On a coordinate plane, a parabola opens down. It has an x-intercept at (negative 5, 0), a vertex at (negative 1, 16), a y-intercept at (0, 15), and an x-intercept at (3, 0).

On a coordinate plane, a parabola opens up. It starts in quadrant 1, crosses the x axis where the vertex is in quadrant 4, and crosses the x-axis back into quadrant 1.

The function f(x) = −(x + 5)(x + 1) is shown.

What is the vertex of the graph of the function f(x) = x2 + 8x − 2 ?

Which quadratic function is the standard form of the equation shown?f(x) = x + 8 + 2x + 5x2

Given the function f(x) = −5x2 − x + 20, find f(3).

The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.Write the function in standard form.f(x) = 5x2 + 40xFactor a out of the first two terms.f(x) = 5(x2 + 8x)Form a perfect square trinomial. = 16 f(x) = 5(x2 + 8x + 16) – 5(16)What is the function written in vertex form?

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?

Consider the function shown on the graph.

Mary throws a plastic disc to her friend. Her friend catches the disc six seconds after Mary throws it. The table shows the height of the disc at one-second intervals.

The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.f(x) = 4(x2 + 12x) + 10 = 36

What is the axis of symmetry for the function f(x)=7−4x+x2?

Which graph represents the function f(x) = –x2 + 5?

On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (3, 6), has a vertex at (5, 2), and goes through (7, 6).