Algebra 66 - General and Vertex Forms of Quadratic Functions

Professor Von Schmohock introduces quadratic functions, focusing on their general and vertex forms. The lecture explains how constants a, b, and c in the general form affect the parabola's shape and position, while h and k in the vertex form directly indicate the vertex's coordinates. The video demonstrates how to graph quadratic functions using vertex form, highlighting the ease of identifying the vertex and the parabola's direction. The lecture concludes with a promise to explore why h and k represent the vertex's coordinates in the next session.

What is the general form of a quadratic function?

• ax^2 + bx^2 + c

• ax^3 + bx^2 + c

• ax + b

• ax^2 + bx + c

Which constant affects the shape of the parabola?

• c

• a

• b

• None of the above

How does a positive value of 'a' affect the parabola?

• It opens the parabola upwards

• It has no effect

• It makes the parabola wider

• It opens the parabola downwards

In the vertex form, what do the constants h and k represent?

• The slope of the parabola

• The x-intercepts

• The vertex coordinates

• The y-intercepts

How does the vertex form make it easier to sketch a parabola?

• By providing the slope

• By indicating the y-intercept

• By showing the vertex coordinates directly

• By simplifying the equation

What is the vertex of the function 1/3(x - 3)^2 - 1?

• (0, 0)

• (-3, 1)

• (3, -1)

• (1, 3)

What does the sign of 'a' indicate in the vertex form?

• The y-intercept

• The position of the vertex

• The direction the parabola opens

• The width of the parabola