Transforming Quadratic Functions to Vertex Form

What is the general form of a quadratic equation?

• ax^2 + bx + c

• a(x - h)^2 + k

• ax + b

• a(x + h)^2 - k

Why can't the coefficient 'a' in the general form of a quadratic equation be zero?

• Because it would make the equation linear

• Because it would make the equation cubic

• Because it would make the equation undefined

• Because it would make the equation a constant

What is another name for the vertex form of a quadratic equation?

• Standard form

• Completed square form

• Linear form

• General form

In the vertex form of a quadratic equation, what does the 'h' represent?

• The slope

• The y-intercept

• The horizontal shift

• The vertical shift

What is the first step in converting a quadratic equation to vertex form?

• Move the constant term to the other side

• Complete the square

• Factor out the coefficient of x^2

• Replace f(x) with y

When completing the square, what do you add to both sides of the equation?

• The coefficient of x

• The square of half the coefficient of x

• The coefficient of x^2

• The constant term

In the example f(x) = x^2 + 2x - 3, what is the vertex of the parabola?

• (-1, -4)

• (1, 4)

• (1, -4)

• (-1, 4)

What additional step is necessary when the coefficient of x^2 is not 1?

• Subtract the coefficient from both sides

• Add the coefficient to both sides

• Factor out the coefficient from the x terms

• Divide the entire equation by the coefficient

What is the vertex of the parabola for the equation f(x) = 2x^2 - 4x + 1?

• (1, 1)

• (1, -1)

• (-1, 1)

• (2, -1)

Which formula is used to find the x-intercepts when the quadratic equation is not factorable?

• Vertex formula

• Linear formula

• Quadratic formula

• Standard formula