Understanding Parabolas and Their Properties

This tutorial explains how to find the equation of a parabola using its vertex and another point. It covers writing the equation in vertex form, finding the coefficient 'a', and converting to standard form. Two examples are provided to illustrate the method.

What is the vertex of a parabola?

• The highest or lowest point on the parabola

• The midpoint of the parabola

• The point where the parabola intersects the x-axis

• The point where the parabola intersects the y-axis

In the vertex form of a parabola's equation, what does the 'h' represent?

• The x-coordinate of the vertex

• The y-coordinate of the vertex

• The y-intercept of the parabola

• The slope of the parabola

How can you find the coefficient 'a' in the vertex form of a parabola's equation?

• By using the x-intercept

• By using any point on the parabola

• By using the vertex only

• By using the y-intercept

What is the standard form of a parabola's equation?

• y = ax + b

• y = a(x + h)^2 - k

• y = ax^2 + bx + c

• y = a(x - h)^2 + k

What is the purpose of converting a parabola's equation from vertex form to standard form?

• To find the x-intercepts

• To identify the y-intercept

• To simplify calculations

• To find the vertex

In the example with a maximum vertex, what are the coordinates of the vertex?

• (0, -9)

• (2, 3)

• (0, -5)

• (1, 3)

What is the final standard form equation of the parabola in the second example?

• y = 2(x - 1)^2 + 3

• y = -3(x - 2)^2 + 3

• y = 2x^2 - 4x + 5

• y = -3x^2 + 12x - 9