Completing the Square for Quadratics with a > 1

The video tutorial covers the method of completing the square, focusing on cases where the coefficient 'a' in a quadratic equation is greater than one. It explains how to graph quadratic functions, find the vertex, and solve for roots algebraically. The tutorial also demonstrates converting equations to standard form and provides practice problems to reinforce learning. The teacher encourages students to engage in productive struggle and offers study tips for an upcoming test.

What does the negative sign in front of a quadratic equation indicate about its graph?

• It opens upwards.

• It shifts to the right.

• It opens downwards.

• It shifts to the left.

What is the vertex of the quadratic function y = -2(x + 2)^2 + 7?

• (2, 7)

• (-2, -7)

• (-2, 7)

• (2, -7)

When solving for the roots algebraically, what is the first step after setting the quadratic equation to zero?

• Add 7 to both sides.

• Subtract 7 from both sides.

• Multiply both sides by -1.

• Divide both sides by 2.

What is the result of taking the square root of both sides of the equation (x + 2)^2 = 7?

• x + 2 = ±√7

• x + 2 = ±7

• x + 2 = √7

• x + 2 = 7

What is the standard form of the quadratic equation y = -(x + 1)^2 - 4?

• y = x^2 + 2x - 5

• y = -x^2 - 2x - 5

• y = -x^2 + 2x - 5

• y = x^2 - 2x - 5

What is the vertex form of a quadratic equation useful for identifying?

• The y-intercept

• The x-intercept

• The vertex

• The axis of symmetry

What is the first step when completing the square for a quadratic equation with a coefficient greater than one?

• Add the constant term to both sides.

• Divide every term by the coefficient.

• Multiply every term by the coefficient.

• Subtract the constant term from both sides.

What is the value of x in the equation x^2 + 2x = -0.75 after completing the square?

• x = -0.5 or x = 1.5

• x = 0.5 or x = -1.5

• x = 0.5 or x = 1.5

• x = -0.5 or x = -1.5

What is the perfect square trinomial for the quadratic equation x^2 - 6x + 9?

• (x - 6)^2

• (x + 3)^2

• (x - 3)^2

• (x + 6)^2

What is the final step in solving a quadratic equation using the complete the square method?

• Take the square root of both sides.

• Multiply both sides by the coefficient.

• Add the constant term to both sides.

• Subtract the constant term from both sides.