Exploring Key Features of Quadratic Functions

This video tutorial covers the basics of quadratic functions, including key features of their graphs, transformations, and different forms such as vertex and factored forms. It also demonstrates how to use graphing calculators for transformations and quadratic regression to model data. The tutorial provides step-by-step instructions for converting between different forms and checking solutions using graphing tools.

What is the equation of the axis of symmetry for a parabola with a vertex at (1, -4)?

• x = 1

• y = 1

• y = -4

• x = -4

Which transformation results in a parabola being reflected over the x-axis?

• Vertical shift up

• Horizontal shift right

• Reflection over the y-axis

• Reflection over the x-axis

What is the purpose of using transformations on a quadratic parent function?

• To simplify the equation

• To make the graph linear

• To adjust the graph's position and shape

• To find the intercepts

What does a vertical stretch of a parabola affect?

• The width of the parabola

• The direction of the parabola

• The height of the parabola

• The x-intercepts of the parabola

What is the vertex form of a quadratic equation?

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

• y = ax^2 + k

• y = a(x - m)(x - n)

How do you find the 'a' value when converting a quadratic equation from vertex form to standard form?

• By solving the equation for y when x = 1

• By plugging in a point that is not the vertex

• By using the vertex coordinates

• By setting x equal to 0

What does the 'c' value represent in the standard form of a quadratic equation?

• The y-intercept

• The y-coordinate of the vertex

• The x-coordinate of the vertex

• The x-intercept

In the context of quadratic equations, what does 'factored form' help to identify?

• The y-intercept

• The x-intercepts or roots

• The axis of symmetry

• The vertex of the parabola

When graphing a quadratic equation in vertex form, what does the 'k' value determine?

• The vertical position of the vertex

• The horizontal position of the vertex

• The direction of the parabola

• The width of the parabola

Which method is used to calculate the curve of best fit for a set of data in quadratic regression?

• Linear regression

• Quadratic regression

• Cubic regression

• Exponential regression