Understanding Quadratic Functions

The video tutorial explains how to convert a quadratic function from general form to vertex form without completing the square. It identifies the coefficients a, b, and c, calculates the axis of symmetry, and finds the vertex's coordinates. The quadratic function is then rewritten in vertex form, and its accuracy is verified graphically by checking the vertex and intercepts.

What is the first step in converting a quadratic function from general form to vertex form?

• Graph the function

• Use the quadratic formula

• Identify the coefficients

• Complete the square

In the quadratic function, what is the coefficient of x^2 referred to as?

• a

• c

• d

• b

What is the value of 'a' in the given quadratic function?

• 3

• -2

• -5

• 12

How do you determine the x-coordinate of the vertex?

• By setting y to zero

• Using the formula x = -b / 2a

• By completing the square

• By finding the roots of the equation

What is the x-coordinate of the vertex for the given quadratic function?

• -3

• 3

• 12

• -12

To find the y-coordinate of the vertex, what value do you substitute into the function?

• x = 1

• x = a

• x = 0

• x = -b / 2a

What is the y-coordinate of the vertex for the given quadratic function?

• 12

• -5

• 3

• 13

What is the vertex form of the given quadratic function?

• f(x) = -2(x - 3)^2 + 13

• f(x) = -2(x + 3)^2 + 13

• f(x) = 2(x - 3)^2 - 13

• f(x) = -2(x - 3)^2 - 13

What does the value of 'a' in vertex form indicate about the parabola?

• The x-intercept

• The axis of symmetry

• The y-intercept

• The direction it opens

Where does the parabola intersect the y-axis?

• (0, -5)

• (-5, 0)

• (0, 3)

• (3, 0)