Exploring Quadratic Functions in Vertex Form

This video tutorial explains how to solve for 'a' in the vertex form of a quadratic equation when 'a' is not equal to 1. It covers the vertex form equation, the parent function, and how to determine the value of 'a' using given points. The tutorial includes step-by-step instructions for substituting values and solving the equation, followed by verifying the solution with a graph.

What is the vertex form of a quadratic function?

• y = a(x - h)^2 + k

• y = a(x - h)^2 - k

• y = ax^2 + bx + c

• y = a(x + h)^2 + k

In the vertex form of a quadratic function, what do 'h' and 'k' represent?

• The roots of the equation

• The vertex coordinates

• The axis of symmetry

• The coefficients of x

What does it mean if there is no number written in front of the parentheses in the vertex form?

• The value of 'a' is undefined

• The value of 'a' is negative

• The value of 'a' is one

• The value of 'a' is zero

How can you determine the value of 'a' by looking at the graph of a quadratic function?

• By finding the x-intercepts

• By checking the vertical spacing between points

• By checking the horizontal spacing between points

• By finding the y-intercept

What does it indicate if the vertical spacing between points is more than one from the vertex?

• The function is reflected

• The function is stretched

• The function is compressed

• The function is translated

Given the vertex (-2, -4) and a point (1, 9), what is the first step to find the equation of the quadratic function?

• Find the y-intercept

• Calculate the slope

• Find the x-intercepts

• Substitute the vertex into the vertex form equation

What is the simplified form of y = a(x - (-2))^2 - 4?

• y = a(x + 2)^2 + 4

• y = a(x - 2)^2 - 4

• y = a(x - 2)^2 + 4

• y = a(x + 2)^2 - 4

How do you find the value of 'a' using the point (1, 9)?

• Find the midpoint of the points

• Substitute x = 1 and y = 9 into the vertex form equation

• Find the derivative of the function

• Calculate the distance between the points

What is the value of 'a' if 9 = 9a - 4?

• a = 1

• a = 9/13

• a = 2

• a = 13/9

What is the final equation of the quadratic function in vertex form given the vertex (-2, -4) and point (1, 9)?

• f(x) = 9/13(x + 2)^2 - 4

• f(x) = 13/9(x - 2)^2 + 4

• f(x) = 13/9(x + 2)^2 - 4

• f(x) = (x + 2)^2 - 4