Vertex Form of Quadratic Functions

The video tutorial explains how to write the equation of a function in vertex form using a given graph. It starts by identifying the vertex and constants H and K from the graph. Then, it demonstrates how to find the 'a' value by substituting a given point into the vertex form equation. The tutorial concludes by solving for 'a' and presenting the final vertex form equation.

What is the first step in writing the equation of a function in vertex form from a graph?

• Locate the vertex point

• Find the y-intercept

• Determine the x-intercept

• Identify the slope of the graph

In the vertex form equation, what do the variables 'h' and 'k' represent?

• The coefficients of x and y

• The x and y coordinates of the vertex

• The maximum and minimum values of the function

• The slope and y-intercept

Why is it necessary to select an additional point from the graph?

• To calculate the slope

• To find the y-intercept

• To determine the 'a' value

• To verify the vertex

What is the purpose of substituting the additional point into the vertex form equation?

• To find the x-intercept

• To solve for 'a'

• To check the accuracy of the vertex

• To determine the function's range

What is the result of solving the equation -6 = a * 16 + 2?

• a = -1/4

• a = 1/4

• a = 1/2

• a = -1/2

What should you be careful about when squaring negative numbers in calculations?

• Subtract the number first

• Multiply by 2 instead

• Use parentheses to avoid errors

• Always add 1 to the result

What is the final step in writing the vertex form equation after finding 'a'?

• Find another point on the graph

• Substitute 'a' back into the equation

• Check the graph for errors

• Recalculate the vertex

What is the vertex form of a quadratic function?

• y = ax^2 + bx + c

• y = mx + b

• f(x) = a(x - h)^2 + k

• f(x) = a(x + h)^2 - k

How do you verify the accuracy of the vertex form equation derived from a graph?

• By checking the slope

• By comparing with the standard form

• By substituting points from the graph

• By finding the y-intercept

What does the 'a' value in the vertex form equation affect?

• The y-intercept

• The x-intercept

• The direction and width of the parabola

• The position of the vertex