Vertex Form and Quadratic Functions

The video tutorial explains how to find the equation of a quadratic function from a graph in both vertex form and standard form. It begins by identifying the vertex of the parabola and using it to derive the vertex form. The tutorial then demonstrates how to find the value of 'a' by substituting a known point on the graph. Finally, it shows how to convert the vertex form into the standard form by expanding the binomial and simplifying the expression.

What is the vertex form of a quadratic function?

• f(x) = ax^2 + bx + c

• f(x) = a(x - h)^2 + k

• f(x) = a(x + h)^2 - k

• f(x) = ax^2 - bx + c

In the vertex form of a quadratic function, what does the vertex represent?

• The point where the graph intersects the x-axis

• The point where the graph intersects the y-axis

• The lowest point on the graph

• The highest point on the graph

What is the vertex of the quadratic function given in the video?

• (0, 0)

• (-2, 4)

• (2, -4)

• (-4, 0)

How do you simplify x - (-2) in the vertex form equation?

• x - 4

• x + 4

• x + 2

• x - 2

Which point is used to find the value of 'a' in the vertex form equation?

• (0, 0)

• (-2, 4)

• (-4, 0)

• (2, -4)

What is the value of 'a' in the vertex form equation after substitution?

• 1

• -1

• 2

• -2

What is the first step in converting the vertex form to standard form?

• Multiply by 'a'

• Square the binomial

• Subtract 4 from both sides

• Add 4 to both sides

What is the result of squaring the binomial (x + 2)?

• x^2 + 4

• x^2 + 2x + 4

• x^2 + 4x + 4

• x^2 + 2x

What is the standard form of the quadratic function derived in the video?

• f(x) = x^2 + 4x

• f(x) = x^2 - 4x

• f(x) = -x^2 - 4x

• f(x) = -x^2 + 4x

What is another name for the standard form of a quadratic function?

• General form

• Vertex form

• Factored form

• Intercept form