Parabolas on Graphs

Josh graphed the function f(x) = -3(x - 1)² + 2. He then graphed the function g(x) = -3(x - 1)² - 5 on the same coordinate plane. The vertex of g(x) is

• 7 units below the vertex of f(x)

• 7 units above the vertex of f(x)

• 7 units to the right of the vertex of f(x)

• 7 units to the left of the vertex of f(x)

When the function f(x) = 2x² is transformed into g(x) = 2(x - 3)² + 4, the vertex of g(x) is

• 3 units to the right and 4 units up from the vertex of f(x)

• 3 units to the left and 4 units down from the vertex of f(x)

• 3 units to the right and 4 units down from the vertex of f(x)

• 3 units to the left and 4 units up from the vertex of f(x)

What is the effect on the graph of f(x) = x² when it is transformed into the function g(x) = -2f(x)?

• The graph is reflected over the x-axis and stretched vertically by a factor of 2.

• The graph is reflected over the y-axis and stretched vertically by a factor of 2.

• The graph is reflected over the x-axis and compressed vertically by a factor of 2.

• The graph remains unchanged.

If f(x) = x², which function is the result of shifting f(x) 3 units left and 2 units down?

• g(x) = (x + 2)² - 3

• h(x) = (x - 2)² + 3

• j(x) = (x + 3)² - 2

• k(x) = (x - 3)² + 2

If the parent function of f(x) is p(x) = x², then the graph of the function f(x) = (x - k)² + 5, where k > 0, would be a shift of

• k units to the left and a move of 5 units up

• k units to the left and a move of 5 units down

• k units to the right and a move of 5 units up

• k units to the right and a move of 5 units down

Given the parent function f(x) = x², the function g(x) = (x - 1)² - 2 is the result of a shift of f(x)

• 1 unit left and 2 units down

• 1 unit left and 2 units up

• 1 unit right and 2 units down

• 1 unit right and 2 units up

If the function f(x) = (x + 2)² is vertically stretched by a factor of 3, what is the new function g(x)?

• g(x) = 3x² + 2x

• g(x) = x² + 2x + 3

• g(x) = 3(x + 2)²

• g(x) = x² + 6x

The lowest point on a parabola that opens up or

the highest point on a parabola that opens down is called________.

• y-intercept

• Valley

• Peak

• Vertex

What is the vertex?

• (0, - 1)

• (0, 0.5)

• (-1, 0)

• (0.5, 0)

What do we call the graph of a quadratic function?

• parabola

• linear

• cubic

• sinusoidal

Tags

CCSS.HSF-IF.C.7A