Finding Vertex Form of Quadratic Functions

The video tutorial explains how to find the equation of a quadratic function in vertex form. It starts by introducing the concept of a quadratic function with a given vertex and another point it passes through. The tutorial then explains the vertex form of a quadratic equation and demonstrates how to substitute the vertex coordinates into the equation. By using the additional point, the tutorial shows how to solve for the coefficient 'A'. Finally, the derived equation is verified by checking the graph to ensure it passes through the given points.

What are the coordinates of the vertex of the quadratic function?

• (0, 0)

• (2, -4)

• (-2, -4)

• (1, 9)

Through which point does the quadratic function pass?

• (2, -4)

• (0, 0)

• (-2, -4)

• (1, 9)

What is the vertex form of a quadratic function?

• y = a(x + h)^2 + k

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

• y = mx + b

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

• h = 1, k = 9

• h = -1, k = -9

• h = -2, k = -4

• h = 2, k = 4

What is the simplified form of the equation after substituting the vertex?

• 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 next step after substituting the vertex into the equation?

• Find the y-intercept.

• Solve for x.

• Graph the function.

• Find the value of 'a' by substituting the given point.

What equation do we get after substituting the point (1, 9) into the simplified equation?

• 9 = a(1 + 2)^2 - 4

• 9 = a(1 - 2)^2 + 4

• 9 = a(1 - 2)^2 - 4

• 9 = a(1 + 2)^2 + 4

What is the value of 'a' after solving the equation 9 = 9a - 4?

• a = 9/13

• a = 13/9

• a = 4/9

• a = 9/4

What is the final equation of the quadratic function?

• f(x) = 9/13(x + 2)^2 - 4

• f(x) = 13/9(x - 2)^2 - 4

• f(x) = 9/13(x - 2)^2 - 4

• f(x) = 13/9(x + 2)^2 - 4

What does the graph of the quadratic function verify?

• The function is incorrect.

• The vertex is at (-2, -4) and the function passes through (1, 9).

• The function passes through the point (-2, -4).

• The vertex is at (1, 9).