Understanding Parabolas: Roots and Vertex

The video tutorial explains how to graph a quadratic function by finding its roots and vertex. It begins with an introduction to graphing parabolas and finding the points of intersection with the x-axis. The tutorial then demonstrates how to factor the quadratic equation to find the roots and graph these points. It covers multiple methods to find the vertex, including using the midpoint of the roots, a formula, and completing the square. Finally, the video shows how to graph the parabola using the vertex and roots.

What is the first step in finding the roots of a parabola?

• Set x to zero and solve for y

• Set y to zero and solve for x

• Find the midpoint of the x-values

• Use the formula -b/2a

Which of the following pairs of numbers can be used to factor the equation x^2 + 4x - 12 = 0?

• (4, -3)

• (6, -2)

• (3, -4)

• (2, -6)

What are the roots of the equation x^2 + 4x - 12 = 0?

• x = -4 and x = 3

• x = -6 and x = 2

• x = -3 and x = 4

• x = -2 and x = 6

How do you determine the x-value of the vertex of a parabola?

• By using the formula -b/2a

• By finding the average of the y-values

• By setting the derivative to zero

• By finding the midpoint of the roots

What is the y-value of the vertex for the parabola given by the equation x^2 + 4x - 12?

• -16

• -12

• -8

• -4

Which formula can be used to find the x-value of the vertex of a parabola?

• x = b/2a

• x = -a/2b

• x = a/2b

• x = -b/2a

What is the purpose of completing the square in the context of finding the vertex?

• To find the roots of the equation

• To rewrite the equation in vertex form

• To determine the axis of symmetry

• To calculate the y-intercept

When completing the square, what value is added and subtracted to form a perfect square trinomial?

• The sum of the roots

• The product of the roots

• The square of the constant term

• The square of half the coefficient of x

What is the axis of symmetry for the parabola x^2 + 4x - 12?

• x = 2

• x = -2

• x = 4

• x = -4

Which method is NOT mentioned as a way to find the vertex of a parabola?

• Using the quadratic formula

• Using the formula -b/2a

• Completing the square

• Finding the midpoint of the roots