Graphing Quadratics in Vertex Form

This video tutorial covers the transition from graphing quadratics in standard form to vertex form. It reviews the parent graph y = x^2 and explores how coefficients affect the graph's shape, including vertical stretch and compression. The tutorial explains the vertex form equation and how to identify transformations such as shifts, stretches, and reflections. It provides step-by-step guidance on graphing quadratics in vertex form and writing equations based on given transformations.

What does vertex form provide over standard form in graphing quadratics?

• More complexity in calculations

• Less flexibility in graph transformations

• Reduced clarity of the vertex location

• Easier identification of graph transformations

What effect does a coefficient greater than 1 have on a quadratic graph?

• Horizontal stretch

• No change

• Vertical compression

• Vertical stretch

What does a coefficient of 1/2 do to the quadratic graph?

• No change

• Vertical compression by 1/2

• Vertical compression by 2

• Vertical stretch by 2

What happens to the graph when a positive constant is added inside the function's parentheses?

• Shifts down

• Shifts right

• Shifts left

• Shifts up

What is the effect of subtracting a number outside the function's parentheses?

• Shifts the graph down

• Shifts the graph up

• Shifts the graph left

• Shifts the graph right

How does a negative coefficient affect the quadratic graph in vertex form?

• Causes vertical stretch

• Reflects over the x-axis

• Reflects over the y-axis

• Shifts the graph downwards

In vertex form, what does the 'h' value represent?

• Vertical shift

• Reflection over the x-axis

• Horizontal shift

• Vertical stretch/compression factor

If a quadratic graph is reflected over the x-axis, what is the sign of 'a' in the vertex form?

• Cannot be determined

• Negative

• Positive

• Zero

What is the vertex of a graph shifted right 3 units and up 4 units from the origin?

• (-4, -3)

• (4, 3)

• (3, 4)

• (-3, -4)

How does adding a positive constant to the end of a function in vertex form affect the graph?

• Shifts it up

• Shifts it right

• Shifts it down

• Shifts it left