Graphing a quadratic function in vertex form with multiple transformations

The video tutorial explains how to graph the equation Y = -1/4X^2 - 5 using vertex form. It covers the components of vertex form, including dilation, reflection, and vertical shifts. The tutorial demonstrates how to determine the vertex, axis of symmetry, and intercepts, and provides a step-by-step guide to graphing the equation by selecting points and understanding transformations.

What is the value of K in the equation Y = -1/4 X^2 - 5?

• -5

• 5

• 0

• 1/4

How does the value of A in the equation Y = -1/4 X^2 - 5 affect the graph?

• It shifts the graph horizontally.

• It reflects the graph over the Y-axis.

• It shifts the graph vertically.

• It stretches the graph horizontally and reflects it over the X-axis.

What is the new vertex of the graph after applying the transformations?

• (5, 0)

• (0, -5)

• (-5, 0)

• (0, 0)

Why does the graph of Y = -1/4 X^2 - 5 not have any X-intercepts?

• Because the graph is reflected over the Y-axis.

• Because the graph is shifted downwards and never crosses the X-axis.

• Because the graph is stretched vertically.

• Because the graph is shifted upwards.

When plotting points for the graph, what is the effect of multiplying by 1/4?

• It moves the points upwards.

• It stretches the points vertically.

• It shifts the points to the right.

• It reduces the vertical distance of the points from the X-axis.