Graphing Quadratic Inequalities and Functions

This video tutorial explains how to solve a quadratic system of inequalities by graphing. It covers graphing the inequalities y > x^2 - 4 and y ≤ x^2 + 2x + 3, finding intercepts, and determining the solution region through shading. The tutorial also highlights the use of dashed and solid lines for different inequalities and provides a visual understanding of the solution set.

What is the general shape of the graph for y = x^2?

• A parabola opening upwards

• A circle

• A straight line

• A hyperbola

How does the graph of y = x^2 - 4 differ from y = x^2?

• It shifts 4 units to the right

• It shifts 4 units upwards

• It shifts 4 units downwards

• It shifts 4 units to the left

What type of line is used to graph y > x^2 - 4?

• Thick line

• Dotted line

• Dashed line

• Solid line

What is the significance of the 'equal to' part in y ≤ x^2 + 2x + 3?

• It indicates a dashed line should be used

• It indicates a solid line should be used

• It indicates the graph should be rotated

• It indicates the graph should be shifted

How do you find the x-intercepts of a quadratic equation?

• Find the vertex

• Use the axis of symmetry

• Set x to zero and solve for y

• Set y to zero and solve for x

What is the axis of symmetry for the equation y = x^2 + 2x + 3?

• x = 2

• x = -1

• x = 1

• x = 0

How do you determine the vertex of a quadratic function?

• By finding the y-intercept

• By using the axis of symmetry

• By setting y to zero

• By finding the midpoint of the x-intercepts

What is the y-intercept of the equation y = x^2 + 2x + 3?

• 3

• 0

• 1

• 2

Where do you shade the graph for y > x^2 - 4?

• To the right of the graph

• To the left of the graph

• Above the graph

• Below the graph

In which region do both inequalities y > x^2 - 4 and y ≤ x^2 + 2x + 3 hold true?

• Where neither graph is shaded

• Where only the first inequality is shaded

• Where only the second inequality is shaded

• Where both graphs are shaded