Graphing Quadratic Equations: Vertex Form and Leading Coefficient

The video tutorial explains how to graph quadratic equations using vertex form and the leading coefficient. It begins with a rocket's height equation, demonstrating how to find its maximum height and when it returns to the ground. The tutorial covers completing the square, understanding the rate of change in parabolas, and the effect of the leading coefficient on a graph. It concludes by solving the rocket equation to determine its maximum height and time in the air.

What is the equation used to determine the rocket's flight path?

• Y = -16X^2 + 96X

• Y = X^2 + 6X - 5

• Y = 2X - 2X^2 - 4X + 3

• Y = -3X^2

How do you complete the square for the equation y = X^2 + 6X - 5?

• Add 9 and subtract 14

• Add 3 and subtract 5

• Add 6 and subtract 5

• Add 9 and subtract 5

What is a common misunderstanding about the rate of change in parabolas?

• It is constant like in linear equations

• It is always decreasing

• It changes by a fixed amount

• It is always increasing

What happens to the graph of y = X^2 when the leading coefficient is 2?

• The graph shifts to the left

• The vertical distance is doubled

• The vertical distance is halved

• The graph shifts to the right

What is the effect of a negative leading coefficient on a parabola?

• The parabola opens downwards

• The parabola opens upwards

• The parabola shifts to the right

• The parabola becomes a straight line

What is the maximum height the rocket reaches?

• 96 feet

• 144 feet

• 32 feet

• 64 feet

After how many seconds does the rocket return to the ground?

• 9 seconds

• 3 seconds

• 12 seconds

• 6 seconds