Mastering Addition and Subtraction of Rational Expressions

The video tutorial introduces quadratic functions, explaining their basic form and graph shapes, such as parabolas. It demonstrates graphing the equation y = x^2 + 2x - 4 by calculating points and plotting them. The use of a graphing calculator is shown to verify the graph. Another example, y = -2x^2 + 3x, is graphed to illustrate the effect of a negative coefficient. The video concludes with observations on how the sign of the coefficient affects the graph's shape.

What is a quadratic function?

• A function with an x term

• A function with a constant term

• A function with an x^2 term

• A function with an x^3 term

What is the vertex of a parabola?

• The intersection with the y-axis

• The highest or lowest point

• The midpoint of the parabola

• The intersection with the x-axis

What is the y-value when x = -3 for the function y = x^2 + 2x - 4?

• -1

• 0

• 1

• 2

What is the y-value when x = 0 for the function y = x^2 + 2x - 4?

• 2

• 0

• -2

• -4

What is the y-value when x = 2 for the function y = x^2 + 2x - 4?

• 6

• 4

• 2

• 0

What is the purpose of using a graphing calculator in this context?

• To find the roots of the function

• To solve quadratic equations

• To verify the graph of a quadratic function

• To calculate the derivative

What is the y-value when x = -2 for the function y = -2x^2 + 3x?

• 3

• 1

• -3

• -5

What is the y-value when x = 0 for the function y = -2x^2 + 3x?

• 1

• 3

• 2

• 0

What shape does the graph of a quadratic function take when the coefficient of x^2 is positive?

• A straight line

• A U-shape

• A circle

• A V-shape

What shape does the graph of a quadratic function take when the coefficient of x^2 is negative?

• A V-shape

• A U-shape

• An inverted U-shape

• A straight line