Exploring Horizontal Transformations in Quadratics

What is the primary focus when discussing transformations of quadratics?

• Determining the coefficients

• Horizontal and vertical shifts

• Graphing parabolas

• Solving quadratic equations

In which form must a quadratic equation be written to easily show a horizontal shift?

• Standard form

• Intercept form

• Factored form

• Vertex form

What changes are made to the quadratic equation to indicate a horizontal shift?

• Modify the constant term

• Adjust the coefficient of x

• Set the B value as one

• All coefficients are squared

How is the vertex of a quadratic equation found?

• (-B/2a, C)

• (B/2a, C)

• B^2 - 4ac

• B/2a

What does the vertex (-0.5, -0.25) indicate about the quadratic's transformation?

• No shift has occurred

• Both horizontal and vertical shifts

• Only a horizontal shift

• Only a vertical shift

What is the vertex of the original function before any transformations?

• (0, 0)

• (0.5, 0.25)

• (1, 1)

• (-1, -1)

How can you determine the type of shift in a quadratic transformation?

• By the sign of the leading coefficient

• By comparing the original and new vertices

• By the discriminant value

• By the degree of the polynomial

What does a change in both x and y coordinates of the vertex signify?

• Translation

• Rotation

• Dilation

• Reflection

What is the result of plugging x = -0.5 into the transformed quadratic function?

• 0.25

• -0.25

• 0.5

• -0.5