Completing the Square Quiz

Why is completing the square a useful technique in algebra?

• It helps in solving linear equations.

• It is only useful for factoring polynomials.

• It simplifies the process of graphing quadratics.

• It is used to solve cubic equations.

What is the vertex form of a quadratic equation?

• Y = a(x + p)^2 - q

• Y = ax^3 + bx^2 + cx + d

• Y = a(x - p)^2 + q

• Y = ax^2 + bx + c

In the vertex form Y = a(x - p)^2 + q, what do p and q represent?

• The coordinates of the vertex

• The roots of the quadratic equation

• The y-intercept and slope of the line

• The x-intercepts of the parabola

What is the first step in expanding a binomial like (x + 3)^2?

• Use the distributive property

• Multiply x by 3

• Square each term separately

• Add 3 to x

How do you determine the constant term to add when completing the square for x^2 + 6x?

• Subtract 6

• Add 6

• Square the coefficient of x

• Take half of the coefficient of x and square it

When converting x^2 + 6x + 11 to vertex form, what is the perfect square trinomial?

• x^2 + 6x + 3

• x^2 + 6x + 11

• x^2 + 6x + 16

• x^2 + 6x + 9

Why do you add and subtract the same number when completing the square?

• To find the roots

• To keep the equation balanced

• To simplify the equation

• To change the equation

What should you do if a quadratic equation has a leading coefficient before completing the square?

• Ignore the coefficient

• Add it to the constant term

• Multiply it by the x term

• Factor it out

In the equation 3x^2 - 24x + 9, what is the first step to complete the square?

• Subtract 9 from both sides

• Factor out the 3

• Multiply by 3

• Add 24 to both sides

What is the vertex of the parabola represented by the equation 3(x - 4)^2 - 39?

• (-4, -39)

• (4, -39)

• (-4, 39)

• (4, 39)