Exploring Quadratic Transformations

What does the vertex form of a quadratic function look like?

• y = ax^2 + k

• y = a(x + h)^2 - k

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

What effect does a negative 'a' value have on a quadratic graph?

• It makes the graph wider.

• It shifts the graph to the right.

• It reflects the graph across the x-axis.

• It moves the graph upwards.

If 'a' is greater than 1, how does it affect the graph?

• The graph becomes narrower.

• The graph shifts to the left.

• The graph becomes wider.

• The graph shifts downwards.

How does a fraction value for 'a' affect the graph of a quadratic function?

• It causes the graph to reflect across the y-axis.

• It makes the graph narrower.

• It compresses the graph vertically.

• It stretches the graph horizontally.

What does an 'h' value of -3 indicate about the graph's movement?

• It moves up 3 units.

• It moves down 3 units.

• It moves right 3 units.

• It moves left 3 units.

How does a positive 'k' value affect the quadratic graph?

• It moves the graph downwards.

• It compresses the graph vertically.

• It stretches the graph vertically.

• It moves the graph upwards.

What does a 'k' value of -4 do to the graph?

• Shifts it 4 units to the left.

• Moves it 4 units up.

• Shifts it 4 units to the right.

• Moves it 4 units down.

If the equation is f(x) = -3(x + 2)^2 + 5, what transformation does not occur?

• Shift up 5 units.

• Shift right 2 units.

• Vertical stretch.

• Reflection across the x-axis.

Given f(x) = 1/2(x - 4)^2 - 7, what is true about the graph?

• It is reflected across the x-axis.

• It shifts 4 units to the right.

• It shifts 4 units to the left.

• It is narrower than the parent function.

Creating an equation from a description: If a graph is reflected, vertically stretched by 5, shifted left 3 units, and up 2 units, what is the correct equation?

• f(x) = -5(x + 3)^2 + 2

• f(x) = 5(x - 3)^2 + 2

• f(x) = -5(x - 3)^2 + 2

• f(x) = 5(x + 3)^2 - 2