Vertex and Quadratic Functions

The video tutorial explains how to convert a quadratic function from general form to vertex form. It begins by identifying the coefficients a, b, and c, then calculates the axis of symmetry to find the x-coordinate of the vertex. The y-coordinate is determined by substituting the x-value back into the function. The quadratic is then rewritten in vertex form, and the process is verified graphically.

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

• Calculate the discriminant.

• Find the y-intercept.

• Graph the function.

• Identify the coefficients a, b, and c.

How do you find the axis of symmetry for a quadratic function?

• Using the quadratic formula.

• By setting the function equal to zero.

• By finding the y-intercept.

• Using the formula x = -b/(2a).

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

• 5/3

• 6/10

• 10/6

• 3/5

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

• By calculating the discriminant.

• By finding the axis of symmetry.

• By using the quadratic formula.

• By substituting the x-coordinate into the function.

What is the y-coordinate of the vertex for the function in the video?

• 120/9

• -120/9

• 40/3

• -40/3

What is the vertex form of the quadratic function discussed in the video?

• f(x) = 3(x + 5/3)^2 + 40/3

• f(x) = 3(x - 5/3)^2 - 40/3

• f(x) = 3(x - 5/3)^2 + 40/3

• f(x) = 3(x + 5/3)^2 - 40/3

Why is it important to verify the vertex form by graphing?

• To determine the axis of symmetry.

• To calculate the discriminant.

• To find the x-intercepts.

• To ensure the vertex and y-intercept are correct.

What is the y-intercept of the quadratic function in the video?

• -5

• -10

• 0

• 5

What does a positive 'a' value indicate about the parabola's direction?

• The parabola is vertical.

• The parabola is horizontal.

• The parabola opens upwards.

• The parabola opens downwards.

What is the significance of the vertex in a quadratic function?

• It is where the function crosses the x-axis.

• It is the highest or lowest point of the parabola.

• It is the point where the function is undefined.

• It is the midpoint of the parabola.