Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the vertex form of quadratic functions, explaining its components and how to graph them. It discusses transformations from the parent function, including shifts and reflections. The tutorial also demonstrates graphing quadratic functions using vertex form, focusing on finding the vertex and axis of symmetry. Additionally, it covers graphing piecewise functions and quadratic inequalities, providing step-by-step instructions and examples.

What transformation occurs when you add a constant to the parent function f(x) = x^2?

• Reflection

• Horizontal shift

• Vertical shift

• Vertical stretch

If the quadratic function has a negative sign in front of the x term, what transformation does it represent?

• Reflection across the x-axis

• Vertical stretch

• Horizontal shift

• Vertical shift

What is the vertex form of a quadratic function?

• f(x) = a(x + h)^2 - k

• f(x) = a(x - h)^2 + k

• f(x) = ax^2 + bx + c

• f(x) = a(x - h)(x - k)

In the vertex form of a quadratic function, what does the 'a' value determine?

• The axis of symmetry

• The y-intercept

• The vertex of the parabola

• The width and direction of the parabola

What is the equation of a parabola that is reflected over the x-axis, shifted 7 units up, and 3 units to the right?

• f(x) = (x - 3)^2 - 7

• f(x) = -(x - 3)^2 + 7

• f(x) = -(x + 3)^2 + 7

• f(x) = (x + 3)^2 - 7

How do you find the axis of symmetry in the vertex form of a quadratic function?

• It is the y-coordinate of the vertex

• It is the x-coordinate of the vertex

• It is the constant term

• It is the coefficient of x

What is the vertex of the function f(x) = (x - 2)^2 + 3?

• (2, 3)

• (-2, 3)

• (-2, -3)

• (2, -3)

In a piecewise function, what does a closed circle at the border line indicate?

• The function has a hole at that point

• The function is continuous at that point

• The function is undefined at that point

• The function has a jump discontinuity at that point

What is the vertex of the quadratic function f(x) = x^2 - 4?

• (-4, 0)

• (4, 0)

• (0, 4)

• (0, -4)

When graphing a quadratic inequality, what type of line is used for a 'greater than or equal to' inequality?

• Solid line

• Dashed line

• No line

• Dotted line