Converting Quadratic Equations from Standard Form to Vertex Form

What is the standard form of a quadratic equation?

• y = a(x + b)^2 + c

• y = ax + b

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

Which form of a quadratic equation is represented by y = a(x - h)^2 + k?

• Standard Form

• Exponential Form

• Vertex Form

• Linear Form

What is the first step in preparing an equation for completing the square?

• Add a constant to both sides

• Subtract a constant from both sides

• Multiply both sides by a constant

• Divide both sides by a constant

In the equation y - 5 = x^2 + 8x, what is the value of b/2?

• 16

• 4

• 8

• 2

What is the vertex form of the equation y = x^2 + 8x + 5 after completing the square?

• y = (x - 4)^2 - 11

• y = (x + 4)^2 + 11

• y = (x - 4)^2 + 11

• y = (x + 4)^2 - 11

Why is it necessary to factor out the negative sign in the second example?

• To eliminate the x term

• To change the direction of the parabola

• To ensure a is positive for completing the square

• To simplify the equation

In the equation y - 2 = -x^2 + 4x, what is the value of b/2?

• -4

• 2

• -2

• 4

What adjustment is made to the left side of the equation when a negative 4 is added to the right side?

• Subtract 8

• Add 8

• Add 4

• Subtract 4

What is the vertex form of the equation y = -x^2 + 4x + 2 after completing the square?

• y = -(x - 2)^2 + 6

• y = (x + 2)^2 - 6

• y = (x - 2)^2 - 6

• y = -(x + 2)^2 + 6

What is the main purpose of converting a quadratic equation from standard form to vertex form?

• To simplify the equation

• To find the y-intercept

• To solve for x

• To make graphing easier