Understanding Quadratic Functions

The video tutorial explains how to find the equation of a quadratic function in vertex form. It starts by identifying the vertex and another point through which the function passes. The tutorial then demonstrates substituting the vertex coordinates into the vertex form equation and solving for the coefficient 'A' using the additional point. Finally, the derived equation is verified by checking the graph of the quadratic function.

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

• (2, 4)

• (-2, -4)

• (1, 9)

• (0, 0)

Which point does the quadratic function pass through?

• (-2, -4)

• (1, 9)

• (2, 4)

• (0, 0)

What is the general form of a quadratic function in vertex form?

• y = ax + b

• y = a(x + h)^2 - k

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

What values are substituted for h and k in the vertex form equation?

• h = 1, k = 9

• h = -2, k = -4

• h = 0, k = 0

• h = 2, k = 4

After substitution, what is the simplified form of the equation before finding 'a'?

• y = a(x - 2)^2 + 4

• y = a(x - 2)^2 - 4

• y = a(x + 2)^2 + 4

• y = a(x + 2)^2 - 4

What is the value of 'a' after substituting the point (1, 9) into the equation?

• 13/9

• 9/13

• 1

• 3

What operation is performed to isolate 'a' in the equation 9a = 13?

• Subtract 4 from both sides

• Multiply both sides by 9

• Divide both sides by 9

• Add 4 to both sides

What is the final equation of the quadratic function in vertex form?

• f(x) = 13/9(x - 2)^2 + 4

• f(x) = 9/13(x - 2)^2 + 4

• f(x) = 13/9(x + 2)^2 - 4

• f(x) = 9/13(x + 2)^2 - 4

How is the correctness of the quadratic function verified?

• By using another point

• By comparing with a standard equation

• By checking the graph

• By solving algebraically

What are the coordinates of the vertex on the graph?

• (2, 4)

• (0, 0)

• (-2, -4)

• (1, 9)