8 Transformations You MUST KNOW to graph a quadratic

This video tutorial covers the essential transformations needed to graph a quadratic function. It begins with an introduction to quadratic graphing and the importance of understanding the parabola and axis of symmetry. The tutorial explains how to use a table of values for graphing and explores various transformations, including shifts, reflections, and scalar multiplication effects on the graph's shape. The video concludes with a discussion on horizontal reflection, emphasizing the importance of these transformations in understanding quadratic functions.

What is the vertex of the basic quadratic function y = x^2?

• (1, 1)

• (-1, 1)

• (0, 0)

• (2, 4)

How does the graph of y = -x^2 differ from y = x^2?

• It opens downwards.

• It shifts up.

• It opens upwards.

• It shifts down.

What happens to the graph of y = x^2 when you add 3 to the function?

• It shifts 3 units down.

• It shifts 3 units to the right.

• It shifts 3 units to the left.

• It shifts 3 units up.

What is the effect of adding a positive constant outside the quadratic function?

• Shifts the graph down

• Shifts the graph up

• Reflects the graph

• Stretches the graph

If y = (x - 2)^2, how is the graph of y = x^2 transformed?

• Shifted 2 units down

• Shifted 2 units up

• Shifted 2 units to the right

• Shifted 2 units to the left

In the vertex form y = a(x-h)^2 + k, what does 'h' represent?

• Vertical stretch

• Horizontal shift

• Horizontal stretch

• Vertical shift

What effect does multiplying y = x^2 by 2 have on the graph?

• It reflects horizontally.

• It shifts horizontally.

• It stretches vertically.

• It compresses vertically.

How does the graph of y = 1/3x^2 compare to y = x^2?

• It is horizontally compressed.

• It is vertically stretched.

• It is horizontally stretched.

• It is vertically compressed.

What is the result of multiplying the quadratic function by a negative inside the function?

• Horizontal stretch

• Vertical stretch

• Horizontal reflection

• Vertical reflection

Which transformation does not change the appearance of a quadratic graph?

• Vertical reflection

• Horizontal reflection

• Horizontal shift

• Vertical shift