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Transformations of Quadratic Functions

Transformations of Quadratic Functions

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to transform the equation y = x^2 into y = x^2 + 10x - 3 by completing the square. It identifies the vertex of the new parabola and describes the translation needed to map the original parabola onto the new one. The transformation involves a translation by the vector (-5, -28), moving the vertex from (0, 0) to (-5, -28).

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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in describing the transformation from y = x^2 to y = x^2 + 10x - 3?

Determine the axis of symmetry

Calculate the integral

Complete the square

Find the derivative

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is completing the square necessary in this transformation?

To find the y-intercept

To simplify the equation

To convert the equation into vertex form

To determine the slope

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the vertex form of the equation y = x^2 + 10x - 3 after completing the square?

y = (x + 5)^2 - 28

y = (x - 5)^2 + 28

y = (x + 5)^2 + 28

y = (x - 5)^2 - 28

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What mathematical operation is used to find the vertex form of a quadratic equation?

Factoring

Completing the square

Integration

Differentiation

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of finding the vertex form of a quadratic equation?

To determine the y-intercept

To find the maximum or minimum point

To calculate the slope

To solve for x-intercepts

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the coordinates of the vertex for the transformed parabola?

(-5, -28)

(5, -28)

(-5, 28)

(5, 28)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How does the vertex of the original parabola y = x^2 compare to the transformed one?

Both are at (-5,-28)

The original is at (-5,-28) and the transformed is at (0,0)

The original is at (0,0) and the transformed is at (-5,-28)

Both are at the origin

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