Understanding Quadratic Functions and Parabolas

The video tutorial explains how to graph a quadratic function in standard form by identifying key components such as the vertex, axis of symmetry, and y-intercept. It provides a step-by-step guide to finding these elements and sketching the parabola. The tutorial also covers how to calculate additional points for accuracy and verify the graph using software.

What is the effect of a positive 'A' in the standard form of a quadratic function?

• The parabola opens downwards.

• The parabola opens upwards.

• The parabola becomes a straight line.

• The parabola does not change.

If the vertex form of a quadratic function is given as (x - h)^2 + k, what are the coordinates of the vertex?

• (k, h)

• (-h, k)

• (-k, h)

• (h, k)

How do you determine the equation of the axis of symmetry for a quadratic function?

• Set y = k

• Set y = 0

• Set x = h

• Set x = 0

What is the y-intercept of a quadratic function if the equation is y = 1/2(x - 2)^2 - 3?

• (0, 2)

• (0, -3)

• (0, 1)

• (0, -1)

What is the first step in finding the y-intercept of a quadratic function?

• Find the vertex

• Set x = 0

• Set y = 0

• Find the axis of symmetry

What is the significance of the axis of symmetry in graphing a parabola?

• It is the point where the parabola intersects the x-axis.

• It is the lowest point of the parabola.

• It divides the parabola into two identical halves.

• It is the highest point of the parabola.

If a point is two units to the left of the axis of symmetry, where is its mirror image located?

• At the same point

• Two units to the right of the axis

• Two units above the axis

• Four units to the right of the axis

How can you find additional points on a parabola?

• By evaluating the function at different x-values

• By guessing

• By drawing random points

• By using only the vertex

What is the y-coordinate of the point on the parabola when x = 6 for the function y = 1/2(x - 2)^2 - 3?

• 7

• 9

• 5

• 3

Why is it useful to plot additional points when sketching a parabola?

• To verify the shape and accuracy of the parabola

• To make the graph look more complex

• To make the parabola wider

• To confuse the viewer