Quadratic Functions and Graphing

This video tutorial explains how to graph quadratic functions in standard form, ax^2 + bx + c. It covers the characteristics of parabolas, including how the sign of 'a' affects the direction of the parabola, and how to find the vertex and axis of symmetry. Two examples are provided: one with a positive 'a' value and one with a negative 'a' value, demonstrating how to plot the y-intercept, find the vertex, and determine the domain and range.

What does the coefficient 'a' in the quadratic equation ax^2 + bx + c determine?

• The axis of symmetry

• The x-coordinate of the vertex

• The y-intercept of the parabola

• The direction in which the parabola opens

How can you find the y-intercept of a quadratic function in standard form?

• By setting y to zero and solving for x

• By calculating the square root of c

• By finding the opposite of b over 2a

• By setting x to zero and solving for y

What is the formula for finding the axis of symmetry in a quadratic function?

• x = b/2c

• x = a/2b

• x = -b/2a

• x = c/2a

In the function f(x) = x^2 - 2x - 3, what is the y-intercept?

• (0, 2)

• (0, -3)

• (0, 3)

• (0, -2)

For the function f(x) = x^2 - 2x - 3, what is the vertex of the parabola?

• (1, -4)

• (1, 4)

• (-1, 4)

• (-1, -4)

In the function f(x) = -5x^2 - 10x - 2, what is the axis of symmetry?

• x = 1

• x = -1

• x = 2

• x = -2

What is the vertex of the parabola for the function f(x) = -5x^2 - 10x - 2?

• (1, 3)

• (-1, -3)

• (-1, 3)

• (1, -3)

What is the domain of a quadratic function?

• All negative numbers

• All positive numbers

• All real numbers

• All integers

For a parabola that opens upwards, what can be said about the range?

• y is equal to the vertex's y-coordinate

• y is greater than or equal to the vertex's y-coordinate

• y is less than or equal to the vertex's y-coordinate

• y is not related to the vertex's y-coordinate

If a parabola opens downwards, what is true about the range?

• y is not related to the vertex's y-coordinate

• y is equal to the vertex's y-coordinate

• y is less than or equal to the vertex's y-coordinate

• y is greater than or equal to the vertex's y-coordinate